Is it possible for a dealer without GST registration to purchase from the other state?

NO!

GST limit of Rs.20lakhs is applicable for under intrastate sale or transfers. Good and Service Tax Law expressly needs registration beneath GST Law for the transfer of goods in the interstate sale.

Traders, thus, won’t be able to avail of threshold exemption of Rs 20 lakh turnover, if they need inter-state supplies.

Then they’ll need to register. Threshold exemption is just for traders WHO are trading among the state.