Hello Mr. Standard.
It is legal to send any debt to a collection agency.
However, in this case the collection agency has very little power. It is unlikely Bovada has your social security number, and thus it will be difficult or impossible to put this on your credit.
The collection agent is not someone you can reason with. They bought this debt at a fraction of its value, and are only interested in your money. They do not care about your individual situation or whether you really owe the money.
Next time the collection agent calls you, instruct them that this is a matter related to an illegally operating foreign gambling site, and is no more a valid debt than one to a drug dealer. Inform them that they must stop calling you, and threaten to call the police if they continue.
Just in case, you may want to check your credit in a few months by visiting
http://www.annualcreditreport.com, which is free.
If you see anything on there that shouldn't be, simply write to the appropriate credit agency and they will remove the item. In this case, you would simply state that an illegal offshore website fraudulently charged you and tried to extort money out of you via a shady collections agency.
However, it is unlikely to appear on your credit.
On a related note, I would advise against charging back to Bovada, as you will be banned for it. As they are likely to be the best poker option in the US for the foreseeable future, you do not want to burn that bridge.
However, if you wish to make amends with them, do it with Bovada itself, and not this slimy collection agent, and only agree to do so if they unban you.