They will be concorded if they attack you, but they will only gain suspect status if they rep him.
But thats the difficulty in fighting with baits.
First off, a support ship, like a logistics ship, has a lot of range when it comes to repairing. Remote shield/armor repairers have like 60km range. So even if you try to take out his support ship, he may be playing cat and mouse with you while his main ship beats down on you and kills you.
Secondly, once you attack the support ship, you will be in a limited engagement with that ship as well. He may warp off and switch ships to a tougher, larger DPS ship and come back and fight you.
Again, its not really recommended unless you have backup as well. But if youre okay with losing your ship, id say go for it.
I lost my navy drake back in 2013 cause i wanted to try killing someone who was baiting.