It looks like Tampa Bay is really interested in him but he may be a good addition to the team on multiple fronts.
Last year, the team averaged 22.6 yds/return on kickoffs and 10.4 yds/return on punts. We scored only one time in the return game. Nearly 80% of the KO returns were handled by Brandon Tate who will not be resigned. Punt returns were split nearly 50/50 between Tate and Adam Jones. In comparison, Washington averaged 29 yds/return on kickoffs and 8.7 yds/return on punts. He scored once as well. Looking at the three-year average, the Bengals have 22.3 yds/return on kickoffs and 10.0 yds/return on punts. Washington meanwhile avereaged 26.2 yds/return on kickoffs and 10.3 yds/return on punts. So overall you can't really argue that he's a major upgrade for the team in the return game and at age 31 it's unlikely he'll improve his numbers this upcoming season.
What about the running game? He had only 36 touches out of the backfield last year and averaged 42 touches over the last three years. His yds/carry were 4.2 and yds/catch were 6.9. Those are slight improvements over Brian Leonard but again nothing extraordinary.
So is he a fit? Yes, if you want to carry four RB's which means one less WR. Washington could assume the 3rd down role although I'm assuming that is the plan for Peerman. His true value is having a proven backup in the punt return game (or the primary returner if Adam Jones isn't resigned). All in all this would be a pretty neutral signing but as a released veteran, his signing would not hurt our ability to earn comp picks for the departures of Lawson, Gradkowski or Sims.