Will I get a bigger mortgage if employer pays for monthly truck loan?

When the balance of your truck loan is at ZERO that is when the bank considers it paid off. Who makes the monthly payment is not relevant to the bank. Your employer could fire you tomorrow... and then you still have an outstanding balance of 20K on the truck.

Not really. 

There is still the risk associated with possibly taking over the payment for the truck (i.e., your employer goes bankrupt, fires you, you quit...). Mortgage banks will include the payment as part of your expenses.

According to Revenue Canada procedures, you are receiving an additional taxable benefit of $500 per month. If you do not pay the tax on it, you will owe a lot in back taxes, penalties, and fines.

No. You are only going to get as much as you qualify for, or what you ask for if that is less.

Only the lender you apply to can give you an accurate answer.

In the US, it is doubtful a lender would accept this. What if you stop working for that employer for some reason and the 'payment agreement' also stops? Lenders are unlikely to take that risk.

Also, in the US, the IRS would consider those payments to be compensation and you would have to report that $6,000 a year and pay any taxes due. That extra $500 a month would raise your debt to income ration a little but not by enough to boost your buying power.

Canada could be different. Which is why you need to get answers directly from the lender.

No.

It's your loan in your name.  You are legally obligated to pay for it.

Your employer could fire you tomorrow and you'd still owe your truck loan.

Your debt is yours and it will be taken into consideration when applying for a mortgage.

No, they are not changing their lending guidelines over a letter. If its in your name, its your loan.