No. This may come as a surprise for some but see CRA’s explanation.

Policy Commentary
Release Date
August 19, 1992
Reference Number
CPC – 006
Subject
Gift-in-kind – Whether the fair market value of an item donated to a registered charity or other qualified donee includes taxes paid by the donor
Purpose
To clarify the Directorate’s policy regarding the establishment of fair market value.
Commentary
The fair market value of an item does not include taxes paid on purchasing the item. Taxes are a cost incurred by the purchaser and are payable to the Crown. The seller merely acts as an agent of the Crown in collecting the taxes. For example, a donor purchases an item from a dealer, pays sales tax and GST on the transaction, then subsequently donates the item to a registered charity. The amount entered on the official donation receipt should be the fair market value of the item before taxes.
References
• Gifts and Income Tax, P113.
• Income Tax Regulations, C.R.C. 1978, c. 945, subparas. 3501(1)(h)(ii) and (1.1)(h)(ii).