Yeah I mean I don't want to debate the merits of the free card in general. But in this hand if we are never folding our double gutter + overcards (as we shouldn't) and we are reasonably sure we can check behind on a blank turn (player dependent), then I'd say it is worth investing another small bet on the flop.
Understand the "free card" play circa SSHE 2004 doesn't often work these days.