As fluketamer said... "Yes it can".
Sorry if this gets a little technical, but it is worth understanding what goes on so you can deal with a stalled fermentation (if indeed that is your problem).
If I read your numbers right, your original SG 1.050 juice would have about 110g/L of fermentable sugar. The 2lb of sugar per gallon adds another 230g/L so the end result is 340g/L of sugar. Now this is a bit of rough arithmetic, but according to Vinolab your starting point is a SG of over 1.100 and potential alcohol over 17% ABV… a hydrometer is your friend! Do those numbers sound about right?
Yeast needs nutrient in the form of YAN (Yeast Assimilable Nitrogen) for a strong cider fermentation, but the only YAN that you have (without adding nutrient) is in the juice. The sugar doesn’t contribute any, so if the yeast runs out of YAN they simply stop working.
To quote Claude Jolicoeur, "apple juice is generally poorer in natural nutrients than other fruit juices". Research has shown that about 10ppm (10 mg/L) of YAN is needed for yeast to ferment 10 gravity points (SG 0.010). So, to fully ferment your juice the yeast would need to start with over 100ppm of YAN, and you might have just fluked it with the smaller batches. The problem here is that although different AJs typically have 50 -100ppm of YAN, some apples have less than this. Also, apples from old unfertilised trees, late picked and very ripe apples can be low in YAN. As well, I understand that juice that has been in cold storage for some time (such as store-bought juice) may develop a depletion in YAN levels and you usually don't know what the blend is. i.e. “shop bought juice” can be a mystery and have some of the above issues. You certainly can’t rely on having 100ppm of YAN.
I have experienced stalling due to nutrient depletion where fermentation stops around 1.010 - 1.020 since my own orchard apples suffer the "tripple whammy" of being from old, unfertilised trees and are generally picked late in Fall when they are ready to drop naturally.
A readily available nutrient is DAP (Diammonium Phosphate) which is about 20%YAN, so adding 50ppm of DAP (50mg/L which is 10mg/L YAN) per 0.010 of required SG drop should move a stalled fermentation along. For "insurance" I will sometimes add a gram (a bit less than 1/4 teaspoon) of DAP per 5 litres at about half-way through fermentation (i.e. SG 1.020 - 1.030) to ensure that I end up at 1.000. Adding DAP at the start can result in a fermentation frenzy which really isn’t desirable. The dosage of other nutrient compounds like Fermaid is about the same.
So, it seems to me that your cider may simply have simply run out of nutrient. Adding DAP or similar should fix the problem.
Phew, I hope that makes sense to you.