A sentence is a certain type of clause, called an independent clause. There are clauses of dependent type that aren't sentences. Really, the only difference between が and でも in connectivity, is that が forms a complex sentence with two independent clauses joined (が is a conjunction), and でも is used to start a sentence, but not join two, so it's used with simple sentences as well as complex sentences.
でも、彼女が遅くまで遊んでたので昨日その顔も見なかった。
The above is an example of a complex sentence with でも. The two clauses joined together are でも、彼女が遅くまで遊んでたので (dependent) and 昨日その顔も見なかった (independent). The first one is dependent because of ので. Note, however, these types of utterances do occur on their own sometimes in speech, so you may hear quite often something like 明日試験があるので, where this is either an answer to something, or the second part is left implied ("I have to go study", "I need to go to bed", etc.).