There's a full breakdown of the rules involved here, but basically a team's entitlement to compensatory picks hinges upon them losing more qualifying unrestricted free agents than they bring in.
We break down the current outlook for the Jets after the jump.
Let's first consider potentially qualifying free agent gains:
Remembering that players cut by their previous team (ie Dimitri Patterson and Chris Johnson) don't count and that guys on minimum salaried contracts usually don't count (ie Jacoby Ford), there were still three free agent gains that should count: Michael Vick, Breno Giacomini and Eric Decker. In the unlikely event that any of these players were cut before week 10, then they might not qualify, but this realistically only applies to Vick because the others are on multi-year deals. Playing time isn't likely to be enough of a factor in the formula to prevent any of these players from qualifying and, as we learned this year, if you end up on injured reserve, you can still qualify even if you're on a one-year deal. It's therefore extremely unlikely that the Jets will have fewer than three qualifying gains.
Now let's turn our attention to qualifying losses:
With the news earlier today that Aaron Berry signed with the Browns, there's a perfect example of a player that would have counted towards the compensatory pick calculation but now does not because he signed after June 1st. Of the players that did sign earlier, there are just three that potentially qualify: Vladimir Ducasse, Isaiah Trufant and Austin Howard. Antonio Cromartie does not count because he was cut by the Jets. As noted above, guys who sign for the minimum usually don't qualify so Ducasse might not count. I'd also suggest that Trufant isn't exactly guaranteed to stick with the Browns either.
All told, the Jets have a maximum of three qualifying losses, so there's no way losses can exceed gains. In certain situations, teams with an equivalent number of gains and losses do qualify for a seventh round compensatory pick, but that should not apply to the Jets because that tends to be when the net value of the losses exceeds the value of the gains.
In summary, the Jets are almost certainly NOT going to receive any UFA compensatory picks in the 2015 draft.