Depuis qu' il est petit, il adore les sucettes. (Since he was small, he's loved lollipops.)

No! I don't think so.

Depuis que as I understand it makes reference to a time earlier which is continuing now.

I understand that "depuis" is used with the present tense.

It would be nice to have an expert comment though.

Hope that helps.

Alan

Not an expert, but depuis can be used with other tenses as well:

Elle ne m'a pas téléphoné depuis quelques jours. -- She hasn't called me since several days. 

There's even a lesson on kwiziq: Using the compound past (Le Passé Composé) vs the present (Le Présent) in negative sentences with "depuis" (since/for) in French