If I get the same boff power on two different boffs, will I get two seperate icons on the power tray that I can use indenpendently of each other?

Yep, you'll get two separate icons to sue as you have two separate powers to use.
Might be worth checking what the cooldowns are like though, some (like Auxiliary to Structural) have a global cooldown as long as the system cooldown so having more than one is a waste of BOff space. If it's a power like Emergency to Shields then it'll enable you to run that power constantly.