I think I would since it's just for a week. Sure the antibiotics are going to kill the probiotics so it's kind of a waste, but yeah, if you figure out when to take each then part of the day you'd have the probiotics to digest your food. I'd guess you'd want to take the probiotics some time (an hour?) before your biggest, most nutrient dense or whatever meal. And take the antibiotic quite a while after the meal is digested and nutrients absorbed. You'll have to do some research on how they work (how long the antibiotic takes going through the digestive tract, when it gets absorbed into the blood stream, etc.
This might be a good time to try intermittent fasting.