Practically speaking, no.
MakeHuman is a decently large, complex code base written in Python against particular specific UI APIs and conventions. Unreal is a very large, complex code base written in C++ against completely different UI APIs and conventions. It would probably be extremely difficult to "integrate" MakeHuman into Unreal as a runtime character generator. Prohibitively so.
You'd almost certainly have an easier time building your own runtime character generator directly inside Unreal.
Further, just because MakeHuman is open-source doesn't mean there will be no legal issues. MakeHuman is released under a specific license (AGPL) which imposes certain requirements on its use. Your intended use may violate those requirements, and the license for MakeHuman may also conflict in various interesting and subtle ways with the license for Unreal. You'd want to double-check the licensing very carefully, possibly getting a lawyer to review it and your intended use.