Yeah, you will have a hard time keeping up unless the Arab is unusually fast, or unless the gaited horses are unusually slow.
My horse is a MFT and I've been riding with Paints, QHs, and a Paso Fino for years. Pasos are gaited, yes, but they move completely different to most American gaited breeds... they're about the same speed as a non-gaited horse.
You will either have to trot every once in a while to catch up, or they'll have to stop and wait for you. It's worst at the walk. Although gaited horses naturally trot and canter faster than non-gaited horses, it's a little easier to stay at the same speed. I don't like to make my horse walk slower than she wants to, so I just stop and wait or make the other person trot.
So yes, it is annoying sometimes, but I wouldn't go out and buy a gaited horse if you don't want one just so you can keep up with them.