It isn't theoretically impossible at least, in light of the recent post on hexamine reduction -
Post 378615
(Organikum: "hexamine to methylamine a old new way?", Methods Discourse) - but I doubt that it would be possible to add the hexamine and ketone at the same time to an Al/Hg mixture - but you may be able to do it as a one-pot reaction, as in first adding hexamine and Al/Hg, followed by the ketone and more Al/Hg when the reaction is over.
However, for best yields and purity, first make your methylamine and purify it, then use it for reductive amination.