Does the word “umpty” have two different meanings?

Umpty is a rare word and does not have a well-established meaning. The vast majority of uses in the Google corpus are as a nonsense word or placeholder (e.g., “Mr. Umpty Ump.”). The Online Etymology Dictionary notes the placeholder sense “of an indefinite number” (1905) and how it relates to umpteen (1917, WWI army slang). This latter word did catch on, with the related meaning “relatively large but unspecified in number.”

In summary:

• Umpty means “placeholder” or “unspecified number.” It is not a common word.
• Umpteen means “unspecified (large) number.” It is a relatively common word.