Famous composers mimicked other composers plenty, or parodied other composers, copied them or played homages. Mimicked, yes, famous composers definitely did mimic other composers.
Prokofiev Symphony No. 1 is one of the more famous. It mimics Mozart and Haydn (obvious choices!)
Stravinsky’s Octet is another.
There are plenty of other examples. Those are just two of the more obvious ones. Bach did it. Beethoven did it. Mozart did it.
I guess the subtle distinction here is that these great composers probably did it because they simply could do it as one deliberate choice among many. Lesser composers may be stuck mimicing a few styles because they lack the skill to go beyond them.
But if some unpublished work mimics a certain style, I would assume that it is an exercise to gain a better understanding of that style.
Prokofiev Symphony No. 1 is one of the more famous. It mimics Mozart and Haydn (obvious choices!)
Stravinsky’s Octet is another.
There are plenty of other examples. Those are just two of the more obvious ones. Bach did it. Beethoven did it. Mozart did it.