NO, NO, NO, NO!
Adobe Illustrator is not, repeat not, repeat yet again NOT a general purpose PDF file editor. It doesn't fully support the entire PDF imaging model. The only PDF files that Adobe Illustrator can safely edit are PDF files saved from the current or earlier versions of Illustrator that have been saved with the “editability” option specified. Anything else is a total crap shoot at best. Text might be converted to outlines or rasters. Colors may be changed (Illustrator only supports either CMYK+spot or RGB+spot+grayscale – no mixtures). Content may be lost. This is not speculation on my part. We hear about such file mangling on a regular basis from customers who are under the misconception of Illustrator being a PDF file editor!!
The method for fixing the problems posed by @Thomas Geist is to use use Preflight in Acrobat which allows you to globally change colors. You can specify the particular CMYK values that you want to change to CMYK=(0,0,0,1) for example or even if you exported your PDF (hopefully using PDF/X-4) with both CMYK and RGB and the black was RGB=(0,0,0), you could use a Preflight Fixup to convert RGB=(0,0,0) to CMYK=(0,0,0,1). You may need to create a custom fixup from the available base fixups, but it is easily doable (I do this quite frequently for this type of situation and other color mishaps) and you will not ruin your PDF file as editing in Illustrator quite often does!!!