DD1 has a birthday on 6th October and she invited friends from school to her party when she was in reception - the teacher gave us a list so we could make sure we invited all the children she wanted to come. I think we invited all the girls and the boys she had known before she started school. We already knew some children from nursery, less than half I suppose. Anyhow almost everybody came most parents stayed - it was a good party and everybody enjoyed themselves.
DS has his birthday on Sept 5th. We have always invited everybody including those children we dont know. I have always put my phone email and address for the mums with a note expressly to say please call me so I can introduce myself. I also invite them to stay at the party and also older/yonger brothers and sisters. In fact when DS was 5 we hired the church hall invited 30 kids and then the brothers and sisters stayed and some parents, in fact we had fifty people in the end! So in answer to your question yes I would let DS go because I have to do the same.
He will be 10 this year and is starting a new school. So I have booked his swimming party for 18th Sept as school doesnt start till 7th and will invite his old friends, all the new kids and some others from other places. Its always worked for us and nobody has ever refused on the basis they didnt know me or DS.