The chord is also used in Eb...I think GtrDave said it best in one of the recent post I read, theory doesn't always dictate what you can play and where, however I don't think 1 chord determines the key. Maybe T-Block will chime in 'cause I haven't been studying music for more than a minute lately...(sorry)...so my advice/instruction may not be the best.
No, one chord does not determine a key center at all, but each chord does have a specific tonality and is derived from a particular scale.
In the case of a dominant chord (7 or 9 or 11 or 13) it is typically voiced as a V and therefore is related to or derived from the mixolydian mode. This does not mean that the key that said chord is in is the I of the V chord. We just went through this on another forum where a particular solo section alone of a song had 6 different dominant chords. The key does not bounce around 6 times as a result.
Instead, the chords have to be taken in context, at the very least by a particular number of measures and/or phrases, to determine what the key center is.