If you're talking about a fixed amount of gas in a constant volume, then yes, pressure is proportional to temperature. Note that the condition for this is that n/V is constant, not simply V. If you just added more gas to the volume, so that you doubled the pressure without changing the temperature, the rate of effusion would change though T doesn't.
But I was talking (as I assumed you were) about the general case, where P, V and T are not specified. In that case you can't simply say effusion is proportional to sqrt(T); you have to state the dependences on P and T explicitly.