As long as it's been imported, ie it says it was registered (in the uk)after it was first used it's obvious it's been imported - mine also says mx5 on the log book, but that it was first used / made in 92, but registered in 02.
The mk1s don't need a cat for the mot, they only need a pre cat emissions test. However, it does still need the lambda to lean the mixture on cruise as it runs a basic closed loop system. If the lambda isn't working, on cruise and idle it will run rich and fail even the pre cat test.
What If There Were No Hypothetical Questions?