Incorrect, PM. Enigma is absolutely correct.
Article 25.4e of the FIA F1 tyre regs says:
At the start of the race each car which took part in Q3 must be fitted with the tyres with which the driver set his grid time. This will only be necessary if dry-weather tyres were used to set the grid time and if dry-weather are used at the start of the race
I would surmise that the intermediates would be too difficult; and it would be dangerous for them to set a time on the inters. The compound in the inters is a different one; and the chemicals and oils inside work differently. Inters have a lower optimum temperature than the dry slicks; and because of the wet conditions, inter tyres are made to be able to heat up more easily as the water will cool them. Without this cooling effect from the water (as in your scenario the track is dry), and the greater ease with which inters can build up tyre temperature you will soon have overheating tyres.
Overheated rubber becomes kind of bubble-gummy; kind of like an eraser. It in itself doesn’t have much grip left. This would also build to a great buildup of tyre pressure. (due to the added heat). This kind of bloats the tyres and they “balloon.” This would mean that although there is roughly the same area of rubber in contact with the track, the amount of rubber is actually less; again, less grip. Also, if the core of the tyre (as opposed to the surface; imagine if you will a steak; at times you find the crust and the inner “core” of it at different temperatures) gets too hot you’ll start to get the surface breaking apart from the tyres; which is what we know as blisters.
Blisters themselves are not actually a performance issue (contrary to what some people believe). The rubber kind of “falls apart” on the tyre and that leaves patches where there are no rubber (kind of like bald patches in hair). The only performance concern of a blister is actually that reduced amount of rubber in contact with the road. However this begins to form kind of like a “perforated line” along the tyre; and so you’re dangerously close to a tyre structurally failing, and that, along with the loss of grip of the tyres makes it very easy to bin the cars.
Basically, in a nutshell, running inters on a dry track (at speed) will mean a lot less grip, and you’re liable to structurally damage them