It is not uncommon for GPs to take any management fees they are owed, and then use it to fulfill part or all of their GP commit, if such GP commit is based on cash. However, note that in most cases, the GPs take the management fees first, pay any taxes due on it, then contribute for the GP commit.

There are potentially tax-advantaged ways to set this up (depending on domicile and tax regulations), but this typically requires custom legal work and discussions with expert tax and fund counsel beforehand - needless to say such are usually expensive and administratively burdensome.