Can the requirement of registration be waived when providing an immoveable property as collateral?

If you want specific answer or precise opinion then you may have to post the question with some details to understand your intention and reason to render proper opinion. 

Your question is devoid of details. 

Here is the Affidavit that I want to check if it will be valid without registration:

I, Mr. A. Patel, Residing at .... Ahmedabad, Gujarat.., ... agrees to the following:

I want to borrow Rs. .....  from Mr. M. Shah at interest rate of ...% per annum.

I own a flat in ... which is valued at ... by a government certified valuator and it is attached here.

I am presenting the following guarantee/collateral:

I agree that if I sell my flat, I will first satisfy the loan obligation to Mr. M. Shah from the sale proceeds.

I agree that this Affidavit, though not registered, has the full force of law. I voluntarily waive defenses for lack of formal registration.

The unregistered affidavit is not enforceable in law hence it will not be accepted as collateral security for the loan.

If in case of mortgage loan the deed should be executed by a registered document in which the collateral security details will be mentioned 

Affidavit is not an agreement, it is only a uniliteral act and no unilateral act can create ownership or possession of property. If you want to create equitable mortgage, pawn or pledge to Mr.M.Shah, you have to give him the necessary documents of your title to M.Shah, and not simply an affidavit, but if Mr.M.Shah, accept your affidavit and gives you money depending on your affidavit that is well and good for you, and I dont see any reasons why anyone should object to it.

Thank you both.

The  money was already loaned and is due now but the borrower is reneging. Can it be recovered now based upon this Affidavit?

Yes, you can file money suit against him, and the burden of presumption and proof is upon you to make your evidence asmissible in court. All the best.