Can colon (":") character be used in shapefile field names?

Field name restrictions inside a shapefile are determined by dBase limitations. There are four single rules:

1. Up to 10 character max.
2. First character in field name must start with a letter.
3. Field names are unique.
4. And, from Understanding DBF Essentials

(...) they can contain any combination of the letters A through Z, the digits 0 through 9, the colon (:) (in dBASE II field names only), and the underscore (_).

ESRI Shapefile works with dBase III+.

According to the same Esri article that you cite:

These limits are imposed so that ArcGIS is able to function with the maximum amount of data types.

Consequently, even if you are not prevented from using the colon in a field name by whatever software you are using to create shapefiles, you will be unwise to use them with ArcGIS.