Is unique_ptr guaranteed to store nullptr after move?

Yes, you can compare it to nullptr after the move and it is guaranteed to compare equal.

From §20.8.1/4 [unique.ptr]

Additionally, u can, upon request, transfer ownership to another unique pointer u2. Upon completion of such a transfer, the following postconditions hold:
— u2.p is equal to the pre-transfer u.p,
— u.p is equal to nullptr, and
...

(the member p is described earlier as — a unique pointer is an object u that stores a pointer to a second object p)

Yes. From C++2011 Standard Section 20.7.1/4:

Additionally, u can, upon request, transfer ownership to another unique pointer u2. Upon completion of such a transfer, the following postconditions hold [...] [the source unique_ptr] is equal to nullptr...