Is it important for a QHSE professional as a consultant to engage in Sales and marketing procedures and or courses to manage his customers ?

Theoretically speaking NO, as handling the customers is job of Marketing/Sales personnel in an ideal terms. But then Practically the concept of Key Account Management is also used in consultancy business, where you deal with few clients and give them end to end service, including handling of complaints and introducing new ideas. In this they should have some knowledge about handling clients properly.

Also as per market and business conditions, sometimes, one can be pushed to do multiple jobs, to make the process cost effective and competitive.

yes, that is important but it also depends on the area of ​​the company, but it is interesting to get an idea of ​​all the procedures in general