In theory yes. In practice no. But you know this 
Because the original schematics & netlists of the CBM chips have been lost over time. The FPGA contents are all re-interpretations by their various authors of how the Amiga hardware worked taken from the various specifications and from observations using logic analysers etc. Lots of information was undocumented and slowly comes out over time in the form of incompatabilities.
The guts of the original MiniMig especially does not work (buses etc.) how the original Amiga worked.
Thanks Alex, I was hoping you would jump in!
Alex and I both work in ASIC design, by the way.
I am in a bar in China, so if this doesn't make any sense, sorry.
Alex, forgive the simplifications here...
The original custom chips (including CPU) are made of a whole bunch of logic gates which together give the functionality of the original hardware. An FPGA is a soft chip, meaning it has a lot of gates which can be configured by a downloaded file. So, it can behave as any sort of chip if you know at a very low level how it works.
Today we use "high" level languages, such as VHDL or Verilog to write the design. This is not software, it is a description of how the circuit should look - like a circuit diagram. The design tools take this code and build a file which when loaded into the FPGA makes the circuit you describe.
If you know exactly how the original chips were designed, you can make a perfect copy.. well, for most cases of perfect.
For the Atari chips, and some CPUs we have scans of the chips which means we can re-create the exact same logic.
http://www.visual6502.org is a good example.
However, often we simplify things because the original chips were constrained by the pins on the devices, so they split the design between a number of chips. We don't need to do this, and we can make some other simplifications.
So, an FPGA Amiga in an ideal world contains the same circuit as the original, has the same bugs, same timing etc.
Yes, the Replay board uses a Spartan3e FPGA. This is a low end device (hence the low cost of the board) but is still capable of running at clock speeds of 200MHz plus inside if the design is optimised for the architecture.
/MikeJ