Given that your experience is obtained on relevent aircraft types run by reputable airlines - who can be contacted for proof of experience - and your licence conversion goes smoothly, there is no reason why you should not be welcomed with reasonably open arms.
There may be some minor issues: if your experince is shorthaul, say within China, you will be at a serious disadvantage to those who have European shorthaul experience in a considerably busier environment. If, however, your experience is longhaulm you will be pretty much the same as any longhaul pilot worldwide, as we all go to much the same places!
Scroggs