You Might Get More Out of Him in a Different Campaign, But You Won't Be Remotely Useless
Little can universally be said about what you will or will not encounter in the Underdark. In terms of what is likely, a social and social magic oriented character will probably benefit from taking Undercommon, that you should remember that one of the most classic creatures you may have dealings with are Drow, who have advantage against being charmed if that is the sort of magic you want to specialize in (sounds like it is), and that you would probably appreciate having "light" or another light generating cantrip at some point. But only your DM knows, ask your DM. Nevertheless there is no reason it is impossible to have a campaign in the Underdark where nobody speaks Undercommon, you never meet a Drow, and every space you find is, somehow or other, brightly lit.
It sounds like you are imagining that this campaign won't involve a lot of social interactions and/or other non-combat opportunities. This is not entirely intrinsic to the Underdark. You will have to ask your DM to what degree this is accurate or inaccurate.
However, let us assume for sake of discussion that what you are anticipating is somewhat correct. It sounds like non-combat stuff is why you are signing up to be a Bard, a class naturally adapted to social interactions, and generally at least competent in any ability check where they don't have negative stats, though builds will always vary, and, of course, out of combat activities of all sorts often make use of ability checks.
If it is indeed a combat heavy campaign it need not preclude you having quite a deal of fun. First off, even a non-combat oriented Bard can still be perfectly useful in combat unless you are opposed to giving them any such competency. It would actually be hard to find enough entirely social-oriented or other skill oriented spells with no combat utility to monopolize your spells known. Many of the better "diplomancy" spells which you would want (suggestion for example) are going to be useful in combat or in avoiding combat, at least provided you are facing creatures who comprehend a language you speak. Disguise self, which you said you would like to be using, can open up many opportunities to deceive enemies into thinking you are their ally, etc, or even mess with non-intelligent monsters. Beyond this sort of magic, no party member will ever resent bringing along someone who can throw out a healing words and inspiration, and even if you had a negative dex score (about which see below) you could still land some hits with a crossbow or what have you. Coming at it from a different direction, a valor bard or sword bard can probably be built to be just as good a face as any bard other than, perhaps, a glamour bard. Bards get a good number of spells, skills for days, and are probably the class least intended to be hyper-specialized.
On the skill side, provided once again that you are dealing with enemies who can understand what you say, you can persuade, deceive, and/or intimidate your way through things, cause distractions, or otherwise generate strategic advantages through honeyed words and other skillfulness. Furthermore if your group is anticipating little non-combat business then you are all the more likely to be the only one who has invested in certain skills when they are useful. Even beyond actual competency, your fellow players would hopefully recognize when it is your particular turn to shine and let you take the lead. And, of course, charisma is the social stat, and a Bard will want that high for spellcasting and inspiration dice even if they never have a social encounter for the entire campaign.
As alluded to above, unless it is vital to your character concept to have the Bard be useless in combat, he can easily acquire a solid amount of combat utility without sacrificing being a consummate master of all things social. Even in terms of straight fighting you wouldn't really want a diplomancer who can't do a little slight of hand or sneak on occasion, which probably means a modest dex investment, which probably means a workable AC and some proficiency in a ranged weapon or a rapier.
All that said, if the campaign is the combat heavy, social light scenario you seem to be anticipating, then you'd probably do well to save this character for a campaign that is less so, simply because you could have even more fun with him there. If there will be literally no social encounters than I think you know the answer to your own question, though still keep in mind that social skills are relevant with basically any creature that can understand what you are saying doubly so if there are not going to be many creatures who can even understand what you are saying. But that is not intrinsic to the setting. Ask your DM. Also, if your party is small, it might be necessary to squeeze as much combat efficiency out of every character as possible, in which case there is likely a better character concept to pursue. On these fronts you can, once again, really only be certain by talking to your DM.
Finally, if your DM won't give you any hints, remember that you can always swap out spells later (albeit only once per level) and that if you are playing a lore bard you will have the opportunity to decide on three of your skills at level 3, so if you're starting at level one you have a great opportunity to adapt based on the campaign so far.
