I wouldn't risk it myself.
I would add grit rather than sand. I have occasionally spread grit over my (heavy Wealden clay) over the years and together with regular mulching with compost and manure it has helped enormously. My soil is now much easier to work. I was advised not to use sand but I can't remember why.

Hi Lm298 and welcome to GoY. If there is any possibility of the sawdust containing varnish then you should not use on your garden. Take it to the recycling centre. The varnish will taint your soil...

I am not using sand as it contains no nutrients for the garden. I only use sand for drainage around bulbs. I also mix in compost and mulch - am seeing an improvement to the heavy already.

Limestone, bone meal, and/or epsom salts often help, too, by "flocculating" the clay--that is, making the tiny particles stick together in sand-sized clumps.