If you sign him on Day 28, your contract will remain for 2 years, yes. But you don't have to pay any wages on Day 1. You can sell him then. The bonus can be covered then.
On the other hand if you leave him unsigned, releasing him will give no money.
And I feel unsigned players count. This season my 3 lowbies were unsigned, despite that I got a decent draw (but lost in round 1 hehe).