Well to cite an actual IP attorney [0], yes. A sublicense means that you (the licensee / sublicensor) grant somebody else (the sublicensee) the right to use the software, and you can do it under any terms you are permitted by the grant of sublicense.

The MIT/NCSA do place some restrictions on sublicenses ("subject to the following conditions") but I don't see any reason why the Apache license would present a problem as the choice of sublicense.

I am not a lawyer, I am not your lawyer, this is not legal advice.

[0] http://danashultz.com/blog/2010/10/19/what-is-a-sublicense-a...