Yes and no. Most songs that are 'in C' are only 'in C' for the first bit of the tuen. Many songs change keys several times throughout the piece. In simple terms, you can 'only' play notes from C in a song that starts in C up to the point where it changes key (this is not an absolute but, at this stage, it is useful to think in those terms).
[b]The straight answer to your question is no; if a chord says G7 the scales you use need to relate to that and not the home key. They may be the same thing but they may not. [/b]
'In C' sometimes only means that the chart is written with no accidentals in the key signature but, as the chords pass, you will find chords with sharps and flats in them because the song is modulating (moving/shifting) from one key to another. Key signatures only apply to notes not the chord symbols above the stave. SHow tunes using dots all indcate key changes whereas fake book charts rarely do so.
PS there is no such thing as a stupid question, just a question that makes you look stupid