Yes, the players typically have to make the team.
As an example, the Patriots lost unrestricted free agent Jim Miller, who was signed by another team. However, he was cut before training camp, so the Patriots received no compensation.
Please note that the key here is 'unrestricted' free agents. Players released by the team (McGinest, Starks, Poole, for example) don't count, either for or against. Obviously undrafted free agents do not count. There is also a deadline, I believe in late July. Free agents picked up in August don't count. If the Patriots signed Ty Law, he would not count against them because he was released.
Last year the Patriots signed free agents Doug Flutie, Wesley Mallard, and Chad Scott. Not one counted against their compensatory formula because they were each released.
The simplest way to estimate compensatory picks is simple counting.
To date, the Patriots have lost seven unrestricted free agents (and three released players) and gained two unrestricted free agents.
The maximum number of picks is four.
An overly simple yardstick to guess rounds using average annual salary is:
$1mm or less = 7th
$2mm+ = 6th
$3mm+ = 5th
$4mm+ = 4th
$5mm or more = 3rd
Thus, right now the formula is 7-2 = 5, reduce to four.