I would like to import a pdf score into a software tool that recognizes the notes and lets me edit and play the music. Is there any software that can do this?
Music OCR is not an exact science, and you have to learn to edit the results and correct numerous errors to get useable output.
I have seen several people who bought a music OCR program and then gave up on it after they discovered that it doesn't work perfectly and automatically. It takes extra work on your part, but it is generally faster than reading scores yourself and manually entering the music into a music notation or DAW (digital audio workstation) program.
You seem to have an Optical Music Recognition problem!
It's not an easy problem to solve - as a PDF of course contains no other information other than an basic image of the music - and recognising the right shapes, with the many possible styles music can be written in is not a simple problem.
Commercially, Photoscore is the main program I've heard of, which connects into Sibelius. Audiveris appears to be the main open-source option, which would produce MusicXML which you could then import into an open source editor, such as MuseScore.
My personal experience with Photoscore (a good few years ago now, I will say) - is it wasn't especially worth the effort - the level of accuracy made it easier to transcribe the score by hand. Audiveris, I have never tried. If you have access to Sibelius, you may wish to try the free demo: Photoscore Lite, and see if it works for your music.
There is a utility called PDFtoMusic Pro, but it only works with a certain kind of PDF music document. You will have to read the product description. I have found it to be extremely buggy and prone to introducing errors, but still occasionally useful for certain scores.