No, that's not counting auxiliaries (except "-masu"). The "explosion" comes from the fact that many conjugations can themselves be conjugated (e.g. "konai" can be conjugated as an i-adjective). I don't think katsuyōkei should be counted as conjugations because they're not words by themselves. Like, obviously a godan verb has 5 possible root endings but that doesn't mean it has 5 conjugations.

If we're counting auxiliary verbs, my system can recognize more than 4000 verb/adjective endings.