The April 10 deadline is the last date that a player who has officially entered the draft can remove his name and still maintain eligibility. Anyone who declares early can un-declare But that deadline has no implications if you wait to declare at all.
The only difference between declaring before April 10 and after April 10th is that declaring before April 10th gives you the opportunity to back out. If you declare after April 10, you have no choice but to go pro.