Could a swollen cheek be a dental abscess?

Yes. Other things can cause a swollen cheek as well. Some examples are salivary gland infections and salivary stones. Regardless of cause this needs to be evaluated ASAP by a dentist or oral surgeon. Don't wait, if this is a spreading dental infection it can be fatal if left unattended.
Could be... Why not have a local dentist take a look? Then you'll know for sure, and the appropriate treatment can be rendered.
Possibly. But this seems unlikely as the only symptom. Patients typically experience pain, fever, and other signs.
Yes. Other possible auses could be a bloke salivary gland, a parotid tumor and other conditions. This should be evaluated by a dentist, or ent.
Yes. The cause may be from an abscess but there are many other possibilities that only an exam can reveal.