Learn English – Valedictions: “My thoughts go your way,”

Yes, many thanks is perfectly proper, grammatical, standard English. It is appropriate to use wherever "thanks" (as opposed to "thank you") would be acceptable.

It ought to be capitalized, although it depends somewhat on what form it takes. The general rationale is that 'Yours' or 'Yours Truly' is a formalized abbreviation of a much longer and more elaborate 'Your true, humble, devoted servant yadda yadda yadda.' Since it's not actually a clause, as he's claiming, but rather a formalized abbreviation, it ought to be capitalized to indicate the use of the convention. However, if he's using something like 'thanks' or another less formal choice, this is somewhat less applicable (and potentially indicative of an unwise lack of formality in a business setting).