I was in NYC at the time but had a house in Katy under contract right around $60k, and got financing rejected bc I was out of state and it would have been my first home.  

You won't offend the bank with an offer (they will auto-reject) but you may aggravate your agent.  

I spoke to 1031ipx local VP, his position 2 weeks ago after coming back from DC is it is never a sure thing.Once you identify 3 like properties if the outcome is get rejected by all 3, you are ineligible.

I rejected the property based on these findings.

Basically the listing agent is saying if you are really that serious with that offer then put your name on a full contract offer with EMD and proof of funds then I will reject it. 

I was rejected.

It took a while and some due diligence with rejection after rejection, but be prepared and look professional.

When you started advertising it "for rent"; when you started showing it to potential tenants (but they didn't fill out an application); when you received a tenant application (even one you rejected); when you received a certificate of occupancy.

Should I wait to hear back from the employer this week, accept him or reject and move to the next applicant?

The event is sponsored by payment processors (ACH, credit cards, debit cards, gift cards), and they are looking for new ways these services can be used.For example, by working with the credit card transaction processors, we can do things like have budgets setup by category, and have transactions rejected if they go over that budget.