Do two-column format journals publish one column for special cases?

Yes, you can ask, but you will almost certainly be turned down for such a request, because journals do not normally keep separate templates for single-column layouts. Moreover, at the type used by journals, a two-column format is essential because long lines of text are difficult to process. (Readability studies show that about 65 to 70 characters per line works best.)

That said, many journals do have to deal with long equations, and in such cases they will have equations that cut across both columns, and indicate how the text "flows" around the equation. As Jon Custer's comments indicate, if there are enough such equations in a row, the page in question may be set in a single-column format, before reverting back to two-column format after the "run" of equations is broken up.

As an example of how this looks, here's a page from a paper published in Physical Review D:

Some do, some don't. It depends on the journal in question. For example, Monthly Notices of the Royal Astronomical Society state in their instructions:

6.1 Layout

Papers should be formatted with two columns (except the abstract) and single line spaced. A single column layout may be used only if necessary for the display of numerous very long equations. The journal is printed on A4-sized paper.

One should always refer to the author instructions/guidelines and can usually contact the editor to ask for further information if something is not stated or is unclear.