Yes and No.
The most effective inhibitor of protease activity is to use serum-containing media. Adult serum is more effective than fetal serum. The protease activity is likely inhibited by alpha-2-macroglobulin. Buffers or media containing human serum albumin (HSA) are ineffective in suppressing protease activity, even at very high concentrations of protein (>10%).
Collagenase activity is not inhibited by serum-containing media/buffers. The most effective method to reduce collagenase activity is to reduce temperatures. Collagenases will lose about 80% of its maximal activity at 26°C. The use of an ice-cold, serum-containing media should eliminate all the proteolytic activity and reduce the collagenase activity in the enzyme containing solution.