The worst case scenario has to be considered. That would be definitely more than m+1 productions after removing unit productions ( does not change the number of productions ) since we can have more than one production for a given variable.
Eg:
S -> ABC
A -> B | C
B -> C | A
C -> A | B
We have 3 variables A,B,C and there are 2*m productions just considering A,B and C.