State of Arizona

I have purchase money loans on my (now former) primary residence in Arizona, and have relocated and decided to allow it to go into foreclosures. My loans are non-recourse.

Will signing a deed in lieu of foreclosure for the bank affect the bank's right (or lack of) to collect a deficiency judgement? As it stands now the bank can foreclose and not collect a deficiency judgement, however I'm not sure if a deed in lieu of foreclosure will affect that, nor am I sure if there is any benefit of this to me.