No, it won't, because just adding a Shimano front derailleur and chain won't chain the brand name on your SRAM crankset (and the ramps and pins won't perfectly match up with Shimano's). Whether or not you or anyone else could tell the difference is, as noted here by several other posters, a truly worthless discussion. I've used Shimano front derailleurs with Specialized, Truvativ (now SRAM), Stronglight, and Suntour cranksets without issue, though.

Cool. The SRAM yaw FD works with Shimano STIs?

yes, worked with the 105 5700 that came on my bike
dont know if the newer 105 5800 fd works

the 5700 rd doesnt work, diff pull ratio

All of the new 10 and 11 speed groups (4700, 5800, 6800) use a totally different pull ratio for the front derailleurs so I'm pretty certain they won't work.

I assume you mean the right (rear) Shimano 5700 STI won't work with the SRAM Force RD, right? I'm aware of that but not sure what you were really trying to say there.

sorry, yes I mean the 105 5700 front shifting is same as sram

my issue was that on my long club rides, the first half would be at a speed
where I would be in small/13 sometimes 12 but was too lazy to shift to big ring as often the rolling terrain would require shifting back to small ring

whilst during the week I train on a small hill so would use small/23,25,27
so during the week I would use the lower end of cassette and weekend the higher end

I eventually replaced the rest with sram red, never had the occasional half shift like I used to have with the 105 5700
sram is much more snap like

Never used 5700 so can't comment there (Ultegra 6600 is snappy as can be for me, 5800 feels close to that, too, and I have heard many echo your complaints about 5700) but it sounds like you simply had/have the wrong crankset on your bike. Being at the extreme ends for most of your cycling speaks to that. Perhaps try a 46/30 or similar, assuming you already have a compact double, or a compact if you are using a standard double now.