I think part of the answer would at least lie in whether the liver was dissected prior to being placed in formalin. I am not entirely sure what would the result be when extracting from these lightly fixed tissues. I think there are protocols available to isolate RNA from formalin-fixed and paraffin-embedded samples so I would imagine at the very least, you can try one of those. But if I were you, I would extract some of the samples and examine how they look on a gel or bioanalyzer. Good luck.
How big are your tissue pieces? Unless they are thin slices, the formalin probably won't have penetrated to the centre of the tissue in one hour. So you could just extract from the centre and cut off the edges.
If the formalin has penetrated then you will have crosslinking which is only partially reversible. You can still do RT-PCR, but I'd suggest designing primers to produce short amplicons.
You should specify which kind of genes are you looking for with your RT experiments since you put the whole liver it is possible that mRNA degraded before formalin get inside. intact rat liver are not too big and probably the formalin was completed diffused in an hour but still mRNA degrades immediately if no RNAse inhibitors were included. You might take a look on the following paper :
D. Groelz, L. Sobin, P. Branton, C. Compton, R. Wyrich, L. Rainen, Non-formalin fixative versus formalin-fixed tissue: a comparison of histology and RNA quality. Exp. Mol. Pathol. 94(1), 188–94 (2013)