The Chabad rabbis I've met go out of their way to welcome people in. They also have to know that for the Reform movement in particular with their stance on patrilineal descent, there is a non-trivial chance of issues with the halachic status of non-Orthodox Jews. I'm a member of a Reform congregation and when I had to make last-minute seder plans one year, the Chabad rabbi didn't ask any questions when I asked to attend their community seder. I was far from the only person there who was not from within the Chabad community.
I don't know how they handle honors for men; as a woman I'm not going to be offered an aliyah or be counted in a minyan anyway, so any questions about my status don't matter there. A man who is offered an honor can and should decline. If there is only barely a minyan, a man should tell whoever's running things (it might not be the rabbi) not to count him. Unless the person asks why not, there's no need to say anything more.
As for attending classes, a Reform ger should take cues from how they publicize the class. Another answer says non-Jews can't learn torah, but I note that several Orthodox rabbis (from across the spectrum) have taught at Pittsburgh's community-wide tikkun leil Shavuot for the last ten years, so the issue seems more nuanced. If the Chabad rabbi offers (and advertises) a class to the whole community, as our local Chabad rabbi does for JLI classes, then anyone in the community can show up -- either that rabbi doesn't hold by the "no torah study" rule or he has chosen the class content with the possibility of a broad audience.
If you find yourself attending more than a handful of their events, it would be a good idea to let the rabbi know your status. He might even respond by offering to teach you!