Well, yes and no. It is possible to see the "signature" of the mixed state in a measurement of the resistance; if the vortices are moving around you get a finite flux-flow resistance even after going below Tc. However, in reality this effect is tiny compared to the drop in resistance (and in order to see it clearly you need to cool the sample in a relatively large field) meaning the transition should still be very clear (the width of the transition is often used to measure the quality of a superconducting film, for e.g. a thin film of YBCO it should be about 1K).
In some cases several transitions can be seen; this happens e.g. if part of the sample has been damaged or oxygen depleted.
Morever, a susceptibility measurement is usually done at low fields with just a small AC coil meaning there shouldn't be many vortices moving around, one should therefore see a very clear vertical drop if the sample is reasonably homogenous.