Is this a valid sugar test?

I'm waiting for my current batch (English Bitter) to clarify a couple weeks in a corny keg in the frig (38-40 degrees). This is my second batch (DME + steeped specialty grains - hops - dry yeast) and while it's definitely better than my first (Coopers prehopped syrup with dry yeast), it has a bit of a sweet taste to it that I don't care for. I'm hoping it'll go away with time, but from what I've read, I'm guessing ferm temps were too high or there's still some unfermented sugar present. I had it in my closet during fermentation which should have been between 68 and 72 degrees. My LHBS seems to think that any air-conditioned house should be fine, but I've read posts here about 70 potentially being on the high side.

I had it in a ferm bucket for 10 days, then put it in the corny with priming sugar/DME for another 10 days. Next time I'll probably just force carb, but I read natural was better. Now it's been in the frig for 4 days. I'd like to test it somehow to see if there are still fermentable sugars left. I was thinking about putting a sample in a soda bottle, shaking it up to make it go flat sooner, then when I know it's flat, add some bakers yeast, put on the lid and let it sit for a few days. If it's somewhat pressurized when I open it, can I assume that there were still sugars, and that I jumped the gun putting it in the frig?

Also, I plan to bottle from the keg. If I leave the bottles in the closet for a few more weeks, would any leftover sugar get eaten up then, or has my yeast keeled over at this point due to the frig temps?

Thanks in advance!

Your yeast is probably dormant and sitting on the bottom of your corny by now. I don't think they'll be doing much as long as the keg is in the fridge.

What were your original and final gravities? Do you have proper carbonation right now after only 10 days of natural carbonation in the keg?

I meant to include the fact that I forgot to measure the starting gravity. I just used my hydrometer for the first time. It read 1.020 @ 52 degrees F. I plugged that in to an online calculator that gave me 1.0194. Now I'm not sure how the carbonation effects gravity, but the recipe says SG should be 1.049 and FG between 1.010 and 1.013.

I did a half batch so I could do a full boil since my first batch seemed really watered down (I added half the volume of cold water to the first batch to cool it and get 5 gal). This time I used an immersion chiller to get the temp to 72 before adding yeast. So for 2.5 gallons, here's what the guy at my LHBS recommended.

2.5 lbs DME
.25 lbs Crystal Malt
.25 lbs Wheat Malt
.5 oz East Kent Golding @ 60 minutes
.5 oz East Kent Golding @ 5 minutes
11 gram packet of dried Windsor Brewing Yeast by Danstar

My fridge is set at 38 degrees F and I've got the CO2 set to about 9 lbs. I don't have the watered down feel with this batch, but the sweetness is still there. With the first couple of sips, it seems pretty good, but as it warms up a few degrees, the sweetness is more prominent.

Should I take the keg out of the fridge for a couple of weeks or leave it alone? I'd like to bottle it to free up the keg, but I'm not sure what the best move would be at this point.

Did you put the keg right in the fridge after priming? That would not be good. I leave my kegs at fermentation temp for at least a week, preferably 2 before moving them to the cold - if I'm naturally carbing. You might try bringing the keg out, giving it a swirl to rose the yeast and then let it rest for a week

I put it in the fridge 10 days after priming thinking it would be done gobbling up that sugar by then. Next time I'll definitely remember to take my SG so my FG will mean more to me. I may go ahead and take the keg out like you suggested and keep my fingers crossed.

Another thing is sometimes kegs fail to seal properly so all of that nice CO2 being made for carbonation just leaks out. It is generally recommended to hit the newly kegged beer with at least 15 psi of CO2 to properly seat the seals and to make sure there are no leaks. I've had one keg do this to me. My habit is to check the keg after about 3 days to see if any pressure is building up. I just do a quick lift of the release valve to see if it hisses. I've gotten to the point where I can pretty accurately tell the carbonation level by the sound of the hiss.