Yes, there is a seedless version of the Concord. I have not tried it
but some reports indicate that it is inferior to the regular Concord.
Regular Concord should begin bearing by the third year. You need to
talk to your Agricultural extension agent to determine whether or not
they will grow in your part of Texas.

The ornamental plums that I am familiar with are either fruitless or
have small useless fruit. http://davesgarden.com/pf/go/53217/index.html
http://treegrowersdiary.com/plumfacts.html