What is your zone? Those trees are good for zones 7-9. I am in zone 7a, Northern VA; my fuyu is also rated for zone 7, but last winter was extremely cold and my fuyu made more fruit than ever. You should take a look at a pollination chart to see if the plants are compattible. According the "Martha's Secrets" they are both self pollinating so my assumption is that they have both flowers.

I can't answer your question with certainty, but I can say that neither variety is considered a reliable pollen source, and I've never come across any references to either producing male flowers, so most likely you would not end up with seeded fruit. Now occasionally some varieties not known so much as sources of pollen do produce a branch of male flowers, but I have not heard these varieties connected with this tendency.
Yes, seeded fruit is valued and actually preferred by some, but like you, I prefer the seedless fruit

I plan to grow them in a particularly cold microclimate in my desert 9b area with possibly a shade cloth. What is this 'pollination chart' you speak of? I think self pollinating refers more to seedless fruit rather than pollinated flowers.