The recommendation I was heard was to seed alfalfa at least 6 weeks before killing frost.  Sounds like you are less than that?

Combine that with the fact that your soil is dry, and I would say "you are setting yourself up for a mediocre stand at best, failure at worst."  I would wait and do a spring seeding, if it were mine.

*Here*, I always say - was always told - they call them "august alfalfa seedings" for a reason - they are to be seeded in August. For me, Aug 31st* is a firm deadline for seeding alfalfa. Otherwise, wait until spring. 

 * - I do realize this date is geographically related. The point is the same.