they don't allow and this is a new rules which called google display url policy. once they caught you,you will be banned.
It is possible to do this however your quality score will suck and your ads wont show most likely. If its your first time and you get caught you wont get banned, your ad will just be disapproved for inaccurate display url.
The only way to even attempt that is to make a legit campaign first, then go in and put a redirect on the domain name, (don't touch your adwords account, just make a redirect file out of the index.php on the domain). Use that at your own risk though.
If the domain of the redirect URL does not match the display URL your ads will not run. Also if you do a PHP redirect on the landing page, or meta refresh, this also will not work. Your ads will run for a short time and then the campaign will pause. But there is a way around this, took me a year to figure it out. My lips are sealed though
do you mean: adwords link - aff link - merchant site If so, then yes you can, but only if the merchant lets you display for their url