Of course, for nostalgic reasons, the simple answer would be yes. Kevin Faulk is a three time Super Bowl champion, team captain, and has been a Patriot for the last 11 seasons. In fact, on a side note, Faulk is the last remaining Patriot to have donned the royal blue jerseys of the 1990's.
The amazing thing about Kevin Faulk is that he's seemingly got better with age. He was back to his usual role of change of pace/3rd down back in 2010, before a knee injury suffered in week two against the Jets knocked him out for the entire season.
With Faulk out, youngster Danny Woodhead stepped up and assumed Faulk's role as third down back/receiver. The question becomes, since the two have similar skill-sets, is there still room for Kevin Faulk on the roster?
Personally, it's hard to say. If I had to make the choice, I'd probably opt to bring Faulk back for one more year. After all, there isn't much of anything behind BenJarvus Green-Ellis and Danny Woodhead on the roster at this point. If the Patriots were to bring in a couple of bodies, that could change my opinion. For now, if Faulk wants another shot, why not give it to him?