When my friend ask me if I can play an entire song, I always tell them can. But the difference is between playing it as a plain butter cake or a cake with strawberries and cream.
To your question, I would say, "yes, you are a keyboardist". The question is - are you the keyboardist others want? That question depends on various factors - most importantly skills. Also depends on whether you can play the genre the band wants you to play. So, the broader your skills set, the more likely you are able to play for various bands.
Requirements differs for different bands. Let's expand this discussion slightly further. Let's list down what we feel the "perfect keyboardist" should be - ie the requirement or "gold standard" for the perfect keyboardist. Note that nobody is perfect. But lets see if this can spur us keyboardist on to further improvement.
I'll start:
1. Playing skills
Cross genres (jazz, pop, classical etc)
Familiar with different keyboard instrument sound playing styles (lead, strings, piano/epiano, B3, brass etc)
Able to both sight-read (notes) and improvise (based on chords)
Able to operate on various keyboards (be it synth action or weighted keys)
Familiar different brands of keyboards (ie Korg, Roland, Yamaha - various models) - so can play on any locations with keyboards already present