Is it possible to recruit neutral creatures, like mummies, into your army in any of the maps?

Level up your hero, max out their leadership and diplomacy skills. ;)
P.S.: They should join. (This is the easiest way...)

It's clear that the previous message wasn't read carefully – the person is asking about hiring phoenixes, not joining them. ;)

To answer the question directly, this is possible on the "Brave New World" map. Hiring other neutral creatures (including manticores, mummies, black knights, wolves, and phoenixes) is also possible on randomly generated maps created using the fan-made random map generator – IRMG.