You might end up accidentally starting 1-player games when you were going to hit the 2-player start, or vice versa.
You can always keep a keyboard plugged in close by as a temporary solution if you're going to eventually get a coin door, or just hide a couple buttons somewhere (like on a back edge of the panel) that you can push. Even a couple bare cherry microswitches without any buttons on them would do the trick, and you could temporarily attach those with 3M removable foam tape until you find a better solution too.
You can also get little vertical coin drops that are cheaper than a coin door. There are small, self-contained metal slot/return things too, that are cheaper than a full coin door. This is the cheapest I found on Happ:
http://www.happcontrols.com/coindoors/40150000.htmIf you call them and talk to a sales rep, they might make a deal if you can't buy it at the listed price.