Oh boy. This topic never seems to get old. This will take a hot minute to break down.
To begin, we don't all possess the same abilities in the Spirit.
1st Corinthians 12:7-12
But the manifestation of the Spirit is given to every man to profit withal.
For to one is given by the Spirit the word of wisdom; to another the word of knowledge by the same Spirit;
To another faith by the same Spirit; to another the gifts of healing by the same Spirit;
To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues:
But all these worketh that one and the selfsame Spirit, dividing to every man severally as he will.
For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
Right away we gain a lot of insight into the nature of what is occurring in spiritual gifts. First, tongues is not speaking in a way only God understands, as it says diverse tongues and the interpretation of them. This is for the translation of human speech across the world, the tongues of the people. There is a tongue mentioned in the Bible that is what angels can use, but this is not the entirety of the gift, nor is it given to all that have this gift as speaking tongues can as simple as someone that is inclined towards a singular other language on earth.
Next, we see that there are many gifts and not everyone is getting them, let alone all of them. The phrase "dividing to every man severally as he will" specifically calls to this aspect as it is God's will to divide who gets what and to what extent. God may not give you any listed spiritual gift, instead focusing on what Paul says is even greater than the gifts.
1st Corinthians 13:1-13
Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal.
And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing.
And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things.
Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away.
For we know in part, and we prophesy in part.
But when that which is perfect is come, then that which is in part shall be done away.
When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.
And now abideth faith, hope, charity, these three; but the greatest of these is charity.
We can see here that despite having the best of the best gifts in the eyes of man, Paul states that each gift is absolutely worthless compared to what otherwise would be seen as common: faith, hope, and charity. Charity is stated as being the greatest, and it is easy to see why when you read the verse. This is not the modern charity of giving, as the phrasing "And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing." lets us know. This is not a monetary giving, but a love that is giving.
So, to come back around to your question. If a person who speaks in tongues, specifically a language of angels, could one do so in their imagination? We can learn what Paul has to say about this possibility.
1st Corinthians 14:1-6
Follow after charity, and desire spiritual gifts, but rather that ye may prophesy.
For he that speaketh in an unknown tongue speaketh not unto men, but unto God: for no man understandeth him; howbeit in the spirit he speaketh mysteries.
But he that prophesieth speaketh unto men to edification, and exhortation, and comfort.
He that speaketh in an unknown tongue edifieth himself; but he that prophesieth edifieth the church.
I would that ye all spake with tongues, but rather that ye prophesied: for greater is he that prophesieth than he that speaketh with tongues, except he interpret, that the church may receive edifying.
Now, brethren, if I come unto you speaking with tongues, what shall I profit you, except I shall speak to you either by revelation, or by knowledge, or by prophesying, or by doctrine?
This means that the gift of tongues is supposed to be used to aid the church, particularly in communication and interpretation. If this is not present, Paul states that it is a worthless gift and instead you should be doing something that edifies. From this, I would conclude that it is not an available gift to communicate to God in a special language. All languages are already understood by God who formed all of them at Babel and has controlled how they have changed and altered over the centuries. Moreover, we have Christ as our High Priest and the Holy Spirit within us that communicate directly to God the Father on our behalf. There is no lack of communication possible that would warrant a special language to communicate with God.