You can try soaking it first, but I'm not sure it will make much difference. If it was really high in salt/sodium like bacon or corned beef then soaking would remove some of the salt, but not all.
It also depends on what else the injection contained and was for. If it contained phosphates to tenderize, then the phosphates already had the effect and soaking it first won't make any difference. In layman's terms once the salt and or phosphate has bound to the protein structure and had a denaturing effect, it can't go back, no matter how much soaking you do.
Another option is to see if you can find fresh thighs. I think they make better turkey pastrami than breasts anyway.