You should be ok, just. I would sow them direct this time of year, and given the sunny dry weather forecast for the next week or two, make sure you keep them wet, best probably under some enviromesh to keep some of the moisture in.
And one more thing, if your previous didn't show, might be worth spending a pound on a new packet of seeds. Parsnip seeds have a reputation. I had to resow this year, and did it with a new packet.