I can't imagine that it wouldn't work. There is no reason I can think of why it would be structurally sound. And I think a lot of people are a little on the militant side when it comes to converting bras in reference to not allowing any original bra to show. It's almost certainly how I would do it. That said, I've never actually done it on anything other than my chainmail bikini, which was another can or worms altogether.

Good luck with it!

I have in the past created a shaped tube to cover the elasticized parts of the back and they looked fine. I usually do add some elastic to the back (unless the bra is loaded with chain mail) and the result is not at all tacky. I use pony clamps to clamp the cup sides and the back ends to a flat surface while they are stretched, slide a piece of paper under the stretched back, trace a pattern, release clamps. Since you are planning on turning under the ends around an O or D ring, you don't even have to worry about accomodating hooks and eyes.

The Costume Goddess has a guide for beginners that has you covering the TOP of the stretchy nubbins only. The fast way to do this is: pony clamp into stretched position and then attach. The clamps function as extra hands and attaching while stretched means you know your stitches will stretch to fit. But do it quickly - don't clamp it, start it, and wander off for a few days! Here's the quote: 'For a solid, covered strap, cut a piece of fabric the size of the stretched strap, adding ½ inch all around to turn under. Pin fabric to strap, stretching elastic as you do. Hand sew this fabric to the midriff strap with zigzag stitches, which expand and contract with elastic. (Straight stitches will prevent elastic from stretching and result in a too-tight fit.) The stitches should appear long and slanted on the inside of bra and very small on outside. If sewn properly, the finished strap will appear slightly puckered on the side and will expand smoothly when worn. '
and here's the link:
www.shira.net/cg/coverbra.htm

I'm a big advocate of completely covering a bra. You never know what opportunities might arise to perform. What looks great on stage may look too much like underwear to the customer if you have to dance close up at a restaurant or a party. Of course you can always cover the unfinished parts with a vest, but why limit your options?

You'll do fine.

For one bra, I didn't even cut off one bit of the back, and it worked just fine. I wanted the stretch and the option to get the whole bra back at a future date, so I covered the bra in black swimsuit lining (four-way stretch) and left enough of a long strip to cover the back band. Then, I folded the original straps in half and slid the O-ring into the fold. Then, I sewed down the folded ends (whip-stitched back onto the other half of the band to keep the stretch) and pulled the fabric in place to make everything look nice and neat.

For another bra (well, swimsuit bra), I didn't want more stretch (the X-ties were already stretch) and I didn't mind cutting up the bra. So, I cut off the straps after the bit on boning that kept the strap wide. Then, I cut a piece of grosgrain ribbon and folded it over the O-Rings. I then sewed the grosgrain down to what was left of the back strap. Then I covered the bra, including covering over the remainder of the back pieces and the grosgrain ribbon, pulling the fabric through the O-Ring and tacking it down in the back (just needed enough stitching to hold the fabric, since the ribbon was holding the O-Ring).

Personally, I cover the side nubbins not only to keep it from looking like lingerie to your audience (bra fabric seems to be a very specific-looking material that ANY woman can spot from a mile away), but also because when you're a bigger-busted gal like us, stretch & give in your dance bra is NOT your friend. Unlike your daily-wear bras where you like to have a little give in the bra, that very SMALL amount of give can lead way to a very LARGE amount of bounce & wiggle once you start dancing. Not a good thing. After all, that's the whole point of using the twill tape for your straps as well.

I did that with a black bra, left about 2 inches of the stretch side, sewed it onto a large silver ring, and then sewed onto the ring 4 feet long ties of stretch black and silver that cross in back, come around front and cross again and go back and tie in the back. The original back piece is so small it's not noticable at all. I also did the ties on top attached to smaller rings and long ties for a halter.You could always hang some danglys on the back piece if it bugs you.The bra is so comfortable that way, and with a serger I did it all in about 10 minutes!

Pictures of the finished product are in my profile, if you want to see. The new straps turned out very well.

Funny story: My teacher was worried I didn't have it tied tight enough, since I'd tied the bow in the back myself, so she offered to re-tie it for me. She pulled the straps so tightly that my breasts were literally touching my chin and I couldn't move my shoulders forward! I got it tied back more comfortably and it did fine, but I now know my stitches can withstand anything!!