I took my fancy plastic bike with 25C tyres last year, was OK but fell off twice on pools of gravel. Cross bike would be ideal for the terrain but agree with the other comment about being too slow on road sections, also you're supposed to be mimicking a bit of P-R... no cross bikes on P-R.
@Scoot you reckon 25c tyres on a fancy plastic bike would be ok if it's dry? I'm wondering if I can borrow a cross bike from someone...