Many Cat 1 installations are suitable, because it is the absence of redundancy / lighting / LVPs etc rather than basic signal quality that is making that runway / ILS cat 1 rather than higher.
However, not all Cat 1 installations are suitable. They need to be within certain ranges of glide slope (I forget them, off the top of my head, but something like 2.6 to 3.5 but that might vary by aircraft, not sure). Certainly autolanding at somewhere like MRS (?14R IIRC 4.1 degrees) would be a bad call.
Also offset localisers are a no go for obvious reasons.
Anywhere with notams / ATIS etc that warns of unsuitability. e.g. somewhere like DUS during parallel runway ops, or anywhere with particular signal / topography issues.
pb