Nope, it isn't an issue. I was in 7 days straight of rain and the stove worked perfectly. Any rain that went down it quickly evaporated off the hot pipe and very little made it to the fire. If setup and no fire you'll get some water but just dump it out and dry as well as you can then start your fire.
Not only is it not a problem the heat dries things in the tent and makes the tent sooo much nicer. I've got a new Kifaru cylinder stove on order to replace my ss box stove and it might be the piece of new gear I'm most excited about. It'll cut close to four pounds from my pack ! Titanium is worth every dime !
When it's raining, I pull my pipe out of the stove when I leave in the am so water doesn't pool in the stove. If I wake in the night, and the stove is cold, I do the same. Not a big deal; I just don't like dealing with wet ashes when I get back at night.