Yes it may, with the following additions - pay particular attention to the front derailleur bullet:
- New BB to work with the FC-R8000 crankset (you already mentioned this)
- New front derailleur to work with the narrower spacing between the chainrings on the FC-R8000 (it is 0.4 mm narrower than the earlier 11-speed offerings, e.g., FC-R6800). The matching 8000-series FD is the FD-R8000. With your current setup, however, this would not work because your shifters are not compatible with an 11-speed FD. A cheaper option would be to try and see if your current front shifter and front derailleur can be adjusted to work with the new crankset. Also, see the information and the link following the bullet list. There is more information there. There is a question here on this exchange that addressed the use of an 11-speed crankset on a 10-speed FD equipped bike: Shimano 105 crankset
- Probably an 11-speed chain. Usually a one-speed difference can be tolerated, which is why this bullet is prefaced with "probably," but an 11 speed chain will work just fine with the 10-speed rear derailleur and cassette.
The front derailleur/shifter is the question mark. You may be able to use your current FD with the new crankset by adjusting the limit screws to prevent the chain from jumping off the small chainring.
In addition, although Shimano's compatibility chart does not show an 11-speed FD compatibility with your front shifter, another article does indicate that Shimano Tiagra 4700 10-speed road shifters are an exception to what the the compatibility chart indicates. If your Tiagra shifters are 4700 series, definitely worth a second look.
HOWEVER, if your Tiagra shifters work well with your REAR derailleur (5700), they are likely NOT 4700 Series Tiagra, since 4700's don't match up with them, and the same goes for your FD (FD-5700), the Tiagra 4700 shifters only match up with the FD-4700. So you are probably out of luck using an 11-speed FD with your current shifters. You most likely have the 4600 series Tiagra shifters, not the 4700. You are relegated to seeing if your current FD-5700 and Tiagra shifters can be adjusted to work with the new crankset.
Item 8 in the link provided below states: "Exception to this rule are Shimano 11 speed road FDs. They will not work very well with anything but Shimano 11 speed road shifters and Shimano Tiagra 4700 10 speed road shifters. Same goes for Tiagra 4700 FDs."
Compatibility Front Derailleurs