Don’t know about plugs – they could be too short – I always start some off in toilet roll tubes to fill in any gaps in the direct sown parsnips – you have to make sure the roots don’t get too far beyond the end of the roll before you plant them out still in the tubes – the tubes decompose as they grow.
Carrots and Parsnips should be sown direct as they do not transplant very well. The very best alternative is the toilet roll system as Johnboy says. But if your going to want say 200 Carrots or Parsnips your going to need a lot of Loo Rolls.