Are non- tax invoices allowable for income tax ?

No such provision is there in the Income tax act.

How ever you should maintain vouchers (with supporting evidence) for each expenditure in excess of Rs.25/-

So, you cannot restrict them to purchase form registered dealer only.

However, Vat laws of some states like kerala provides for purchase tax for those purchases from unregistered dealers.

Non-Tax Invoices are acceptable for Income Tax for the purpose for claiming deduction. Only the thing is it should be a fair invoice and not mere a quotation or estimate. Further it should be in the name of the assessee. You should also verify the entries in the register if any maintained for receipt of materials, Purchase Orders, GRN Notes etc. to verify genuinness of Purchase. You may also seek third party confirmations.