Yes if they sign more than they lose then you don't get any comp picks, but they will almost certainly lose more than they sign because they have 14 players destined to become UFA!
After the Season the following Pats are set to become UFA:
Hightower
Bennett
Sheard
Blount
Harmon
Bolden
Delevin
Cannon
Long
Scruggs
Vollmer
Mingo
Ryan
and they have an option on Branch that if they decline he too will become a UFA
What I'm saying is that even if the Pats resign a few of these guys, there is still enough talent there that will garner enough contracts to off set any players that the Pats would sign in Free Agency. Now keep in mind excluding the list about, the Pats already have 38 players signed for 2018, plus a draft class of at least 8 more.
The only thing that make sense about this trade is if the Pats they think they will easily reach the max 4 comp picks (without figuring in the loss of Collins) and they traded Collins away to get an additional pick. Because other than that, this trade makes no sense for either team.
I hope all this speculation is wrong and the pick is a "conditional" pick and the condition is that the Browns sign Collins long term. Because if its for a Compensation pick, the Pats will basically get nothing in return for Collins.