Well yes, but mostly no, that depends entirely on the armies, the geographic location, and the year. Celt, Gaul, and Viking armies tended to be more likely to engage one-on-one because they were made up of warriors not soldiers. Even more "developed" countries didn't utilize the pike for a considerable time period.
Pike usage had a big drop off after Alexander the Great and barring a very few showings didn't become a mainstay weapon for armies until about the 15th century. About 900 years or so after the medieval time period began.\
For those interested here's more: https://en.wikipedia.org/wiki/Pike_(weapon)
There's also the fact that the vast majority of casualties in a great number of battles happened during a route. A lot of the killing would be people in very broken formations being chased or shot down by loose but still organized formations of high moral enemies.
Pike usage had a big drop off after Alexander the Great and barring a very few showings didn't become a mainstay weapon for armies until about the 15th century. About 900 years or so after the medieval time period began.\
For those interested here's more: https://en.wikipedia.org/wiki/Pike_(weapon)