I haven't been able to find too much research addressing this question, but one relevant source is "Intervocalic Rhotic Pronunciation by Adult Learners
of Spanish as a Second Language", by Timothy L. Face (2006).
Face compared 41 native American English speakers who were studying Spanish at the university level (I assume at the University of Minnesota, because Face is a professor there) to 5 native speakers of Spanish. 20 of the native English speakers were fourth-semester Spanish students, and so would be considered intermediate learners, while 21 were Spanish majors or minors.
Face found that students in both categories had much higher error rates for the production of the alveolar trill than the native Spanish speakers. The more advanced students were more likely than the intermediate students to mispronounce the trill by replacing it with a tap (which is a Spanish "r" sound, just not the correct sound in the context of the words that were being studied).
Face's introduction also references an earlier study, "English Speakers' Acquisition of Voiceless Stops and Trills in L2 Spanish" by Jeffrey T. Reeder (1998), which looked at data gathered in 1997 from 40 native English speakers learning Spanish at the university level and 5 native Spanish speakers. Reeder also found fairly large differences between the native English speakers' and the native Spanish speakers' pronunciation of /r/.
My impression, based on these two studies, is that it seems likely that a significant proportion of native English speakers have difficulty with consistently using the alveolar trill /r/ in fluent speech in a second language. Depending on how you define "able to pronounce r as alveolar trill", that could indicate that many native English speakers lack this ability. If you use a definition that doesn't require consistency, and just requires somebody to be able to produce the sound at some point, then presumably more English speakers could be categorized as "able to pronounce r as alveolar trill", but I don't know of any studies that focus on that.
The two studies looked at relatively small groups of students, so it's not clear to what extent the results generalize to "native English speakers" as a whole. Nevertheless, I think this at least counts as evidence that the acquisition of trill /r/ is not trivial (as gaazkam's question pointed out, even native speakers of a language with /r/ may take a while to master this sound), so it seems unlikely that monolingual native English speakers, who typically don't acquire this sound as part of learning English, would have the same ability to pronounce it as speakers of other languages that do use /r/ regularly.