The spec for axial play on the intermediate shaft is 0.25mm. 1.0 is a LOT and 4X spec! Measure so you know for sure. Excessive axial play on the intermediate shaft usually means is that the thrust ring on the shaft is broken. If that is the case, then no, that's not ok to run as is. Running with the thrust ring broken runs a very serious risk of ruining/breaking/throwing the timing belt.To be clear, what I am calling the 'thrust ring' is a machined lip of the outer bearing journal of the intermediate shaft. The part that bolts onto the block and holds the intermediate shaft in place, I call the intermediate shaft seal carrier.
The replaceable intermediate shaft bearings affect radial play. They do not affect the axial play. If your axial play is 0.24mm, then it is perfectly fine. If you are concerned about the intermediate shaft bearings, then you could pull the shaft to see. If you do so, you'll want to replace the seal carrier o-ring.