The answer to the question "Are there any characters that conventionally share the exact same width as these ten?" is a qualified "Yes."
Tabular numerals (whether Lining or Oldstyle) are the default in most fonts. They are designed for tables, as in balance sheets, annual reports and similar financial applications. In any given table, the only things that MUST have the same width are the numerals, so only these are designed that way. In most modern typefaces, #, $ and other currency symbols are given the same width as tabular numerals, but nothing else. Even the # and the British pound symbol (which map to the same ASCII number in the old 7-bit code) can be much wider in older typefaces like Baskerville, so this isn't a universal standard.
If you have an OpenType font, look in the Glyphs panel in AI or ID or a similar application for the Lining Figures section. Most of the glyphs (not all) in that section will have the same set width as the numerals. Beyond that, if a given glyph in a particular font happens to have the same set width as a tabular numeral, it is a coincidence. (The equals sign you found is an example.)