I tried FunctionExpand, but it does not do what you want:
Erf[1/2] // FunctionExpand
You can use a replacement rule instead:
erfRule =
Erf[x_] :> 2/Sqrt[\[Pi]] Inactive[Integrate][E^(-t^2), {t, 0, x}];
Erf[1/2] /. erfRule
The expression Integrate[E^(-t^2), {t, 0, 1/2}] is a number, of course. To check it you can use NumericQ, not NumberQ:
NumberQ[Integrate[E^(-t^2), {t, 0, 1/2}]]
NumericQ[Integrate[E^(-t^2), {t, 0, 1/2}]]
