It would be safe. The ILS projects a localizer signal (left/right deviation compared to runway alignment) and glideslope signal (up/down deviation versus the intended flight path, usually about 3°).

The only thing you need a precision altimeter setting for is to determine the safe decision altitude (point at which you need to see the runway environment to continue, else initiate a missed approach) and a fairly theoretical chance to intercept a false glideslope lobe.

With the clear weather, knowing the decision altitude with precision was not important and the false glideslope is easy to identify by comparing outside view and descent rate needed to stay on the glideslope.