The short answer is yes.
Of course, the longer answer depends on what is the ultimate goal? is it to attempt to produce modern replicas with 100% new build parts (or using some percentage of original parts), or is it to attempt to remove the discrete components from a cracked/corroded original board, and replace the board itself, recycling the original parts? Perhaps all of the above?
Anything is possible. PCB manufacturers are cheap nowadays; I regularly get small boards produced out of China: $10 for 10 boards. My colleagues have had slightly higher quality boards produced out of Germany.
The main hurdle to what you are proposing, will be the schematic capture stage. Depending on the vintage of the boards you are copying, many older boards were laid out by hand and parts density is low. This would allow you to visually reverse engineer the schematic from the boards, draw it up in modern software and go from there. If the original boards are a bit more complex, you might need to trace out the original design with a multimeter/oscilloscope and perhaps simulate the resultant schematic in software to make sure it functions as it's meant to.
Another factor is the availability of the discrete parts; many parts are obsolete and discontinued these days, particularly peripheral driver chips. As mentioned in other posts, some parts were specific to the original computer manufacturer.
All things considered, you might wind up with a 1:1 replica, or something with modern components substituted in to preserve the original functionality. It is up to you to consider how 'authentic' such a board would be if you're attempting to sell them; many older oscilloscopes had the traces on the boards laid out by hand with tape, and part of the appeal is the look of these hand laid boards. An example of what I mean can be found on a NES control board, as seen here. So yes it is possible, but 'feasible' depends on your final goal, and how desirable what you're making will be to others if you intend to sell limited production replicas.
As a final note, although I haven't done anything as complicated/rare as an accelerator card, I have done something similar. The company I work for has several 80's vintage analogue front end amplifiers for data logging, many of which now have non-functional channels. I've copied the original schematic, updated the op-amps to more modern high-bandwidth versions and surface-mount versions of some of the parts and had them produced as updated replacements. I've also seen some projects online where people have gutted old game console cartridges, desoldered the eprom chips containing the original game code, and replaced the core chip with another one which has been programmed with a different game. At the time I saw this I considered the feasibility of producing new-build cartridge boards and emulating the CIC chip with something modern like an ARM chip. The idea came to nothing, but it's inline with what you're proposing.