They may not. Most Apple trees must be pollinated with pollen from another compatible variety. It is important that varieties with overlapping blooming times are planted together.

I bought a specialty apple (Sekai Ichi)from a vendor a few years ago who wouldn't sell just one tree. Problem was, he had only one tree left in stock...the only way he would sell to me was if he picked an appropriate companion tree for pollinating.

What is a good apple variety to plant for cross-polination of McCoun?

I don't know about McCoun specifically, but doesn't Rome act as a cross-pollinator for many varieties? BTW, see link for using crabapple as a cross-pollinator depending on early or late blooming.

Here is a link that might be useful: apple cross-pollinators