It could. Live prey triggers their instincts with a lot more scent than f/t prey has. It's generally best to avoid offering any live prey when what you want to feed is f/t.
And if you couldn't get frozen rats of the proper size, why not just feed two or 3 f/t mice?
Remember that when a snake is accustomed to taking f/t (or fresh killed prey), they're more likely to make a mistake when grabbing live prey & getting themselves bitten & injured by the prey.
Along with the increased likelihood of future refusals to eat, you also risk pain, suffering & scars for your pet, & vet bills for you, when you switch between f/t & live prey. But it's your call.