No, not really. Steve CS explains it above, but just to stick my oar in, you're conflating two different things: construction and harmonic function. Strictly speaking, "dominant" is not a flavor of chord, the way major and minor and augmented and diminished are--though as Steve notes it's sometimes used that way, often to distinguish it from a maj7--it's a description of what the chord is doing harmonically. "Major" strictly refers to the way a given chord, regardless of context, is constructed. So a major chord is a major chord regardless of whether it's the tonic, the subdominant, or the dominant at any particular point in the harmony. Thus, a G7 in the key of C (or C minor, for that matter) is a major chord with an added minor 7 that serves a dominant function. And it would have that dominant function even if it didn't have the added F and were a simple G triad.
I guess I internally include 7ths(or 6ths) on every chord whether or not someone is playing it and I separate chord types to help me navigate lines. But I understand what you’re saying!!