Good question. I suppose it could be managed by moving players from the Clearwater roster to the FCL roster, to make room for the draftees; essentially, most of the guys previously on the Low-A roster would get the month of August off.
Keeping in mind that, with a 165 player in-season domestic roster limit, the organization will likely have to purge some guys to make room for the draftees anyway; some of the guys at Clearwater could be moved up, instead of out, at the end of July.
Speaking of which, the domestic roster limit is currently at 175 (the off-season limit). This limit drops to 165 on Opening Day; between this 10-spot reduction and the fact that 14 guys on the 40-man will be optioned by Opening Day... even with injuries, there's going to be some real pressure on the roster limit at the end of March.