Computer architect here. Forget about reverse engineering. Not only couldn’t they reproduce the microprocessor, they couldn’t reproduce the mother board, since it is multi-layer, and there wasn’t technology to do that yet. There are little discrete components on the board that are much smaller than anything back then. The bus speeds also are way higher (forget about the CPU speed.) My bachelor’s thesis, in 1973, was a design for a radio astronomy project that ran at 125 MHz, using expensive ECL components and requiring me to etch my own boards.
Even if someone could reproduce the logic of the PC, there would be so many TTL components with unreliable connections that it would never work. John Campbell had an editorial once called “No Copying Allowed” about what people in WW I would do with a jet fighter - and that was from 1961 or so.
So, what could you do with your PC? If you had the foresight to load gcc on it, quite a lot. It would not be hard to translate Fortran programs into C, or even into a more modern Fortran. Programs back then were not very big, since the computers didn’t have enough memory for a big program. You could run all their code in almost no time at all. I would suspect that you could probably do a lot of the work using Excel, not even a programming language. This was before parallel computers, so the code would be pretty simple. Now if you had a copy of Mathematica you’d be in great shape.
BTW, this was a long time before C. Fortran and assembler were used, COBOL was just beginning, and Algol 60 was being worked on.
Getting the data out is a bigger problem. I doubt that anyone could build any circuitry fast enough to interface with a USB port, or even a serial port. No one had PostScript. Printer drivers assume a lot of intelligence in the printers, which was not there at the time. So, bring a printer, or let the researchers hire some people to copy the output data for later punching into cards.
Oh, and the computer wouldn’t end up in a cryptography lab, it would be at Lawrence Livermore, Los Alamos or Sandia doing nuclear weapons simulations. It could probably break codes while waiting for the nuclear scientists to figure out what to give it next.
Also BTW, batch was heavily used in the early '70s. I used the first Multics system in college, but it was far from common. CTSS was just an experimental tool.
And forget about bringing an Intel engineer back with you. You couldn’t even begin to build a modern fab back then. First of all, there was not technology to make it clean enough. Second, all the fab equipment has computers built into it, computers that don’t exist back then. Knowing the right things to work on might speed the introduction of CMOS, but not by much. To design a computer you need CAD tools running on the previous generation, so all improvements are incremental. I doubt there is anyone at Intel, or anyplace else, who knows even a fraction of what is required to jumpstart a semiconductor industry using 1960’s technology.