Can H4 visa holder work outside of US (remote work in Indian company) but stay in US?

I have H1 visa and GC is under process. My spouse is in India and has 9 years experience in IT and currently working in India.

Can he come to the US on H4 and work remote for the same company in India? (income will be in Indian Rupees and tax will be paid in India)?

No, it is not allowed. If you live in US and work remotely or engage in any sort of work, it is technically non-compliant and you would be considered violating your H4 status…Spouse can work if you can get H4 EAD for your spouse.