Fabsil (synthetic) or Nikwax (water bound wax) will add a bit of initial water repelling structure to the fabric surface. In really wet conditions this will be overpowered and the natural waterproof function of Ventile and similar fabrics (swelling of the fibres to close the structure of the fabric) takes over again. Over use of proofing destroys the ability of the fabric to take up water and swell and thereby spoils the function of the cloth to become self waterproof. If in doubt - do not proof and let the fabric do its own thing!
I have used Ventile for several decades, love it and treasure it and even used it in my final clothing collection when I did my Btec OND in Design: the SASS fabric is a similar fabric. This proofing (or not ) regime should work fine on your smock
Be aware that over spinning the smock in the washing machine could cause seam failure as the spin tries to force lumps of water through an impermeable layer of fabric - so low or no spin - and that your smock will probably hold lumps of water even if you do spin it and pulling the smock from the machine will tip these all over the floor, flooding the utility room floor ... experience here I am afraid...
Pull the smock into shape and line dry it on a hanger ... tumble drying will be long and expensive as the fabric will be wringing wet...