Yea, I don't think T/S will do what the OP has in mind, but it does depend on the framing.
Not sure focus stacking will be perfect either though. You'll likely still need a very small aperture to avoid artifacts around the edge of the flower.
With FS there are basically 2 issues - movement and the OOF foreground masking the background when you are focused on the background. In the latter you essentially end up with a zone around the foreground object where you never get a sharp image. You even see this on some of Helicon Focus' examples.
So, yes in general choose a sharp aperture for focus stacking, but for extreme situations you may have to use f22 and even then some clean-up may be necessary. Also the non-pro version is IMO not useable. You need the editing functionality. It's going to depend on how far the background id directly behind the flower though.
Also Helicon Focus does work in conjunction with T/S (even though you need to have the frames ordered correctly and tilt does 'strange' things). This may be a partial solution to the problem, but will depend very much on the exact framing. I think you'll need some experience with tilt (or a really good explanation which I'm not capable of) to understand why.
If it's just a flower without the stem in the foreground, I would take a shot (or focus stack) of the flower, then get someone to hold the flower out of the way, take another shot(s) of the background and blend them.