Yeah, in that ballpark. The in-season Domestic Reserve Limit (DRL) is full now. If they keep the major-league roster full (40), they'll be optioning 14 players, and they'll need to make room.
The two DSL rosters are limited to 35 players each, in season. They're currently at 24 and 25, so they have room for 21 recent signees - which is the exact number they have signed, excluding Renteria and Parra (who are already DSL rosters). So they're kinda OK there, assuming they don't sign a bunch more international amateurs.
Challenges? The Clearwater roster is heavy (currently 45 guys; in-season limit of 30). The 14 players optioned aren't likely going to Single-A, so unless they start a cascade of demotions, there will be cuts in the AAA or AA rosters, and they'll still have to reduce the Clearwater roster.
Then there's the promotions from the DSL to to either the FCL or low-A. There will probably be some; don't know how many, but these could come at the cost of releases from Clearwater.
The offset to this is players who go "off-roster" when the season opens - guys on the 60-day IL (and any restricted list/suspensions, etc. - if any). Plus any players currently on the AAA roster who are recently-signed spring non-roster invitees, who may have assorted escape clauses if they don't make the 40-man roster (and they mostly won't!).
It looks like the Wilkinson release may have been triggered by the Gillispie signing, to keep them at the 165-player DRL.
It's also possible that additional players have been released in the past day or two, and not posted to the milb transactions pages yet. This could particularly be true of players on the Clearwater roster; in my experience, the Phils' Clearwater minor league staff tends to be slower than the people at the other levels in getting things reported to the front offices in NYC (probably because they have a bunch or spring training and complex responsibilities in addition to managing the low-A roster/organization).