Sinhalese has a ton of - not Pāli words, but Sanskrit words. For example, we say "Viṣuddhimārga" not "Viṣuddhimagga" and "nirvāna" not "nibbāna". But since Pāli and Sanskrit are very similar, it's pretty much like having Pāli words in the Sinhala language. (To my knowledge the way the words are pronounced are not very different from how an Indian Sanskrit speaker would pronounce them.)
In my un-scholarly opinion, North Indian languages seem to have deviated from Sanskrit roots with the influence of the Mughal Empire. If you listen to someone speaking Hindi, for example, you'll hear a lot of 'z' and 'f' sounds - sounds that don't exist in Pāli/Sanskrit. (These sounds used to be absent in Sinhalese, and were added very recently after European influences.) Don't know about Bengali and Nepali, though.
As for spoken Pāli, I do remember reading an interview with the late Ven. Balangoda Ānanda Maitreya, where he said when a Burmese Sayādāw came to Sri Lanka to propagate the Mahāsī method, they conversed in Pāli.
So I guess we can't rule it out completely.
If there are any linguists around, I'd like to hear their opinion, I think it's a fascinating subject.