I don't think that perfusion is usually done.  Rapid transfer of the tissue to dry ice or RNAlater is most important, particularly for those tissues with a high level  of RNAse activity.

http://www.lifetechnologies.com/us/en/home/references/ambion-tech-support/nuclease-enzymes/tech-notes/rnase-activity-in-mouse-tissue.html

Strictly in considering the RNA quality, I think the above answers are solid.  Depending on what you are investigating and trying to isolate, perfusion may help separate your cells of interest from likely contaminants. If you are concerned about blood contamination in your samples and the remainder of your protocol doesn't completely address this, perfusion may provide some benefit.