I have been enrolled in the ARD program in PA due to a dui. I refused the BAC and received a year suspension of license in PA.

It very will could be. Typically the states have an agreement to report license suspensions to each other. So, PA will likely tell DE about it.

PA will notify DE of your refusal. DE will then treat the refusal as if it occurred in DE. You will get a 2 month suspension in PA when you go on ARD. PA will notify DE about the ARD disposition but most likely DE won't do anything about your ARD suspension because it is not a conviction.

I am not licensed to practice law in Delaware, but I think the answer is yes because if Delaware did not honor the suspension, PA's suspension would merely encourage you to continue driving in DE, which may be unsafe.