Oh yes - I always try to sell players through auction. If they don't go after a reasonable number of attempts then they go to sell now.
Thomas Denervaud bought 2 seasons ago as DC/DL with Free-kick SA, age 23, 5*/47Q, for 3T/$4.66M (worth $4.88M) - played 55 matches, 2 MoM, 5 goals, 2 assists, ave. rating 7.11 - sold as age 25, 3*/49Q (worth $4.99M) for $5.32M.
Chris Lux bought 3 seasons ago as GK, age 23, 5*/44Q, for 5T/$4.44M (worth $4.42M) - played 62 matches, 2 MoM, ave. rating 7.21 - sold as age 26, 3*/47Q (worth $4.16M) for $3.9M.
I usually find that x4/x9Q (and sometimes x3/x8Q) players go for a premium after a bidding frenzy, others you make a small loss or break even on, so it all balances out in the end.