I am not a sound man but an electrician. But as I understand it, speakers only receive power. So if you connect 300 watt speakers to a 250 watt amp, you can only get 250 watts out of the speakers. If this understanding is correct, this could not blow your amp.
I might say, however, that in most things electrical, they are not intended to be used at maximum output for very long. So if this understanding stays true with sound equipment, then running your 250 watt amp at maximum output in an attempt to get 300 watts out of it, this could shorten the life of your amp even though you never actually overload it.
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