I agree that the specific verbiage and underlying reality the the game is unfinished are probably not a big factor in preventing people from trying 0AD, but I suspect they might be significant factors in low retention and engagement depth.
As FOSS, there are few good reasons not to install the game and give it a try if you are interested. However, playing around for a few hours will quickly clarify the meaning of those labels. The game is clearly missing some key ingredients of the value proposition of a full-featured RTS (which wowgetoffyourcellphone just listed), and the verbiage of its "unfinished alpha" state communicates that these features are coming, just be patient. Thus if you are bothered by the lack of any of these features you will say to yourself "this is promising, but I'm not going to waste more of my time trying to get enjoyment from a prototype; I'll come back when it is finished."
Thus that notional user never goes on to become a regular multiplayer competitor or a content contributor. They simply lurk, until eventually they forget 0AD exists, or they realize that the timeline for these features to be delivered is not weeks or months like most commercial early-access or games-as-a-service products, but years or decades. The end result being that yes, you got a new user for a few days or weeks, but they did not "join the community," and therefore the community remains small.
Dropping the alpha labeling might help with retaining some of those players, who enjoy their initial experience of the game, but anticipate a better value proposition if they wait to full invest their time. It would at least encourage them to make their own assessment of whether the value proposition of the product is enticing enough for them to stay engaged, rather than defaulting to the word of god that the product is not ready yet. However you are likely correct that the benefit will be small.
I think the bigger benefit will come from how that change would affect the project's development priorities. 0AD can't keep coasting along on aspirations of eventually delivering a complete product in perpetuity. If the project can't deliver on a "full-featured single player campaign," and "a multiplayer environment where we're no longer arguing over what constitutes cheating or not," and "where the civ designs are rather solid and complete and the tech tree not in flux"; then it would at least be healthy to give some thought to what sort of optimal value proposition can be delivered in the immediate future, and focus more effort on developing that. Dropping the "it's sill in alpha" excuse might help motivate that change of mindset.