[Closed] Will many road bike frames...

Very few without going for a modern disk frame or a cyclocross frame, both work perfectly well as road bikes. These are normally classed as endurance or gravel frames in marketing speak.

Most racing specific frames would still struggle to fit greater than 25mm tyres, although this is changing as the Pro peloton was using 28's in some of the classics this year.

35c is pretty big even for touring so I would agree with the chef. If the bike has been designed to take mudguards then you'll stand a better chance of getting a tyre larger than 28c on it especially if the guards haven't been fitted, but even so, you might struggle with a 35c.