Technically yes. They arent removed from your inventory in the place of caps but when before you pay for your items, sell the legion/ncr money to the vendor. The problem with this is that they dont go for their full cap value unless you have high barter or are selling to vendors who are memebers of factions that you have idolized reputation with.
I have trouble selling legion coin to most vendors. NCR money is easy to sell, but many don't take legion coin.
When you trade with anyone you can trade them anything in your inventory, and they'll take NCR dollars or Legion coins at the equivalent rate instead of caps, they just don't take non-cap money automatically. It's easier to have all your money in caps anyway, since any kind of payments done through conversation (buying implants, for instance) has to be done in caps.