[1C-(1H)-1NT 6-9, may or may not have stopper. Alertable?]
I would. The ACBL Alert Pamphlet
has this to say about treatments (natural calls that by agreement pass additional information):
Natural bids that convey an unexpected meaning must be Alerted. This includes strong bids that sound weak, weak bids that sound strong, and all other bids that, by agreement, convey meanings different from, or in addition to, the expected meaning ascribed to them.
The "expected" meaning of 1NT in this auction includes some heart strength; if by agreement, the partnership would bid 1NT with
9xx, I would take that as "different from expected meaning".
The underlying concept of Alerting in the ACBL is your partnership's legal and ethical obligation for your opponents to be able to understand your calls as completely as you do. Therefore, a good guideline, (which happens to be enshrined in the Alert Pamphlet, as well) is:
WHEN IN DOUBT WHETHER TO ALERT OR NOT, ALERT!
(caps and emphasis in the original). So, in both this situation and your other ("takeout" NT doubles), where it is "unclear", Alert. For one thing, that's what you're supposed to do. For another, the TD will be much less likely to rule MI against you if you Alert where you, if you were Solomon, shouldn't (especially if they don't bother to ask) than she will be if you fail to Alert where you should. And finally, you will be doing your ethical best to protect your opponents, which is the key to pleasant, fast, good, respectable bridge.