JBroad: I waited to see if someone else would reply. Guess not.
Playing scales behind a vocalist wouldn't sound very good, in my view. The better method would be to play some sustained notes in the chord (like maybe the flatted 7th if the chord is, say a Bb7 AND that is not the melody note). What you want to avoid is playing the melody and overwhelming the vocalist; instead, support the vocal line by playing in between the phrases, etc. Improvised arpeggios can be tasty if properly placed. Or, you can harmonize with the vocalist, if he/she agrees AND if the vocalist sings a straight melody (which some can't do these days!!).
Not all tunes begin on the tune's tonic chord (a tune written in C may start on another chord) nor do they always end on the tune's tonic chord. If the lead sheet you have does not denote a key signature, then just ask the keyboard or guitar - they probably know it. Soon, you will be able to tell it yourself when you become more familiar with the tune(s).
One thing I've learned - don't always rely on what the vocalist tells you (about keys and starting notes - some vocalists are notoriously wrong - they'll call a tune in C, then immediately begin singing it in some other key and not even know it). It of course depends on the quality of the vocalist (and the back-up band).
It takes some practice and an ability to play at reduced volume to back vocalists, but when done correctly, it is a nice complement to a vocal. DAVE