In that case the president could effectively pardon the companies that declined to collect those taxes. Competing on price, companies would stop collecting the tax if they were free from prosecution.
Again, a pardon is for criminal activities. If the companies decide not to collect nor pay those taxes, they will not be charged with a criminal activity; and so there is nothing to pardon.
When a corporation doesn't pay its taxes, the entities in charge of collecting the tax levy the funds from the corporation's bank accounts first, then ask questions later. The burden is (wrongly) placed on the corporation to recollect funds that were taken from them.
On the other hand, many of the taxes that we pay are constitutionally legal. So while a President may pardon everyone for not paying any kind of tax, and decide not to prosecute those that rightfully should have paid taxes, he would be neglecting his constitutional duties if he did so.
So could a President prevent Congress from collecting any sort of funding at all? I suppose so, but not constitutionally (not that that seems to stop anyone these days), just as Congress, in practice, can make any law they want whether constitutionally authorized or not; and the Supreme Court, in practice, can strike down any law (or make any law, it seems) they want whether constitutionally authorized or not.