Income reported in T4A is considered as scholarship, bursary, fellowship, research award, etc. according to CRA. It is not considered as employment income, therefore, no tax is deducted.
Income reported in T4 is considered as employment income, which is tax deductible.
Although it is not clearly mentioned in CIC instruction and operating manuals, there are cases where application got rejected for showing income with T4A slips instead of T4.
Also, if you look at the checklist , as a proof of employment CIC is looking for T4 tax information slips (not T4A), which means they are particularly giving importance to T4 slips.
I am also Post-doc for about 5 years and i am also receiving T4A. I am paying tax for my Income, which is for the amount mentioned T4A. As per CRA, Post-doc income is considered as a employment/taxable income.
Additionally, Post-docs are in work permit. So I think it will not be a issue, either T4 or T4A. Hopefully, this issue will not reject our application.