USCIS uses the "place of celebration" rule to determine whether a marriage is valid for immigration purposes. If you get anything that is legally considered a marriage at the place where it happens, then you are very likely to have your I-129F denied if there is any record about it. To be eligible for K1, you have to prove 3 eligibility factors, one of which is: you and beneficiary are legally able and eligible to marry within 90 days of beneficiary's arrival to US. By having an existing marriage, you and beneficiary would not be eligible in this regard in most cases.
You may be able to present some novel legal argument to counter that but I'm not sure it's worth all the risk and hassle.
In summary, if you want an easy approval then don't do it. If you want to get married, just get legally married and apply for CR1.