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Yes, The PASMO website (Japanese | English) states one can use a PASMO card across Japan if the transport provider accepts an IC card for travel (indicated by the IC mark on their card readers). This is enabled by the National Transport IC Card Shared Use Service among card issuers.
In other words, if the transport operator takes ICOCA (the IC Card issued in Kyoto and co.), they will take a PASMO card.* The non-exhaustive list of operators includes:
The only downside with using a PASMO card in Kyoto is that station staff won't be able to help you fix any problems related to the card itself, as they are not the card issuer.
Side note: The above applies to both regular PASMO and PASMO PASSPORT (the tourist version) cards, but the latter is only valid for 28 days after issuance.