Of course! Playing most sports will have some carry-over to other sports in terms of your general athleticism.
The younger you are, the more your motor skills will improve. For an older athlete, the benefit will be more in terms of general fitness and athleticism.
Many young athletes specialise too early. Over here in Japan, most youngsters choose one sport and only play that sport for their whole sporting life. And although they practise the same sport all year, they don't really progress any faster than athletes in the Anglo-Saxon countries with our tradition of 2 or more differing sports seasons a year.
Definitely you should play basketball. Even if it didn't really help your football, you said you enjoy it. There you go. And it will stop you becoming a fat whale in the football off season.