Bipolar junction transistor analysis at emitter.

lam58 said:

Although technically wouldn't Vc/Vs = Vc/Vb since R1, and R2 are ignored?

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No, because there's a resistor, RB, between Vs and Vb.

lam58 said:

Would there be no gain since Re is grounded meaning Ve/Vs would = Vs?

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The fact that Re is shorted (not grounded; one end of Re can be grounded without the whole thing being shorted) means that Ve is zero, which means that Ve/Vs is zero.