Can Toroidal-core Transformers be mounted with bolts going directly into the core?
You mention 'laminations', so you're obviously talking about an iron core.

The major issue is that toroidal cores are wound with copper all the way round, for packing efficiency. If you drilled into the side of a standard wound transformer, the drill hole would cut through every winding. This means that a toroidal designed to be mounted this way would need relatively large areas left not wound to allow access, sufficient to maintain insulation integrity to the high voltage windings. That would be a fairly large hit in VA and efficiency, for the 'benefit' of being able to be mounted this way.

A second issue is the reduction in core cross sectional area, which would directly result in a reduction of volts/turn, so further reduce the transformer VA.

A third issue is the one you mentioned of shorting laminations together, which will increase core losses, reducing efficiency.

Electrically grounding the core has absolutely no effect on core saturation.

There's not a lot broke with the clamping method of fixing a toroidal transformer, certainly nothing to be gained trying to fix it this way.