t105 20hr rate 225AH, 5hr rate 185AH, so my guess on a 35AH, drawing 10A, would get it down to 50% or less. so.... depending on construction, could either end up with a pretty short cycle life, dead battery, or nothing to worry about. but a 35AH 12V battery is likely pretty small, lots of very thin plates, not something that likes much discharge current. my guess based on my experience with motorcycle batteries, it ain't gonna work. But all you can do is try.
I do have a 30ish AH AGM battery for my motorcycle. If I was to try to draw 10A out of it for anywhere near 1 hour or even 1/2 hour it would be dead, dead, dead.
Those with this same battery who have left headlights on (5-8A draw) find the battery is to dead to start the bike after about 30 minutes.
CCA is 75A, and it won't do that for more than 10 seconds at a time with a rest and after 20 seconds or so it is pretty weak.