The answer to your question is yes, for the following reason:
There were dual-types and dual-W+R as far back as the EX series. The ruling was made that if Pokemon are weak to one or both types of the other Pokemon, both are checked for.
Since LEGEND Suicune-Entei is weak to Water and Electric, x2 is applied twice, and therefore, it does x4 damage. (The same thing happens if double resistance is involved, which would be -60 - due to double-resistances so far being only in Hoenn Pokemon-ex.)