An hour or two on ice in a baggie is fine. I've left blood samples on ice in a cooler for hours myself, but it is best to get them to the freezer/fridge asap. That was for later use in chemical analysis and the results came back fine - so no big deal.
If the tube does not have EDTA or another preservative it will coagulate very quickly.
I'm pretty sure there are tubes with no EDTA in them, but they probably are specific for protocols in which the EDTA would intract with another chemical during analysis. SO long story short, most tubes already have that preservative in them so that can be an assumption. Anyone who is that interested in the allotted time for blood to coagulate has probably drawn blood themselves and understands this point.
The Ice thing was actually a big beef with me in "I am Legend" (Movie). He didn't give her ice to put the blood sample in...would have been worthless.
My kids appreciated me ruining the end like that...
