If your going to use the Fox for his SP refill service at all- you need to get his social link up. Otherwise- its a cash grenade- even on the best days.
The cost to refill SP is based on the amount you need refilled; the rank of the Hermit Social Link; and the particular mood of the fox on that particular day.
The in-game text implies that he's "healing you". This doesn't actually mean he'll refill your health- he'll just fill up your SP- at least at the low rank I have him at. You'll want to use an SP based healing spell to max out your health before talking to the fox to get your SP refilled.
The fox will also give you a free item- often a very useful one- if you visit it in the Entrance to The TV World and pat it on the head- in just about every mood except for angry.
Also- and Vinny noticed this- Fox has the worst voice acting in the game. Or at least text-to-voice conversion.
Answer me this Mr. Caravella and Mr. Gerstmann: Why do you have to turn everything into a dirty/subtext joke?
As the game goes on- you'll realize- everything that Yosuke says sounds creepy and wrong. Its a major theme.