I can corroborate knaidlach’s claim the chabad spends most of the time learning gemara and halocha.
Though I am not chasidic or lubavitch, I went to a lubavich high school. We spent all morning learning the exact same stuff as the litvish school i had transfered from.
About 1/2 my classmates didn’t take “English” aka secular studies, and I guess they had some tanya classes in the afternoon (I never asked what they learned in the afternoon).
So if they did learn/obsess over geulah, it was at the time that the litvish boys were studying math and history.
I think people think that chabad is overly preoccupied with moshiach because this is a main talking point. Remember that chabad is outward-facing and their chosen tafkid is to push an agenda, and they have been very successful in kiruv.
Chabad is not interested in being mekarev the frum. In fact I believe CS is not here to push her agenda but she is here out if the love of sharing ideas about yiddishkeit, both chabad and others (not guessing, this she stated and i take it at face value).
As for the talking point of moshiach on billboards etc, this is what they believe, and it makes a compelling story intended i think to attract the lost sheep. The consequence of these campaigns seems to rub the non-chabad frum crowd the wrong way. Get over it (please).