First of all you client must have the RIGHT version of Acrobat. I find that clients can some time have unrealistic expectations not only of designers but reality itself.
If your client only has Acrobat Reader ( you know, the FREE thing) he wont be able to do this with your files or anyone else.. no matter what you do.
Now, if they have invested in the full Acrobat Pro, they have TWO options available, assuming you send your files in PDF format ( see: save as PS PDF)
1) Actually this is not available, since PS works in raster and doesn't embed text, but I thought I would mention it anyway. You have the TOOLS>ADVANCE EDIT >TOUCH UP TEXT TOOL. It's really ok.. as long as you haven used any fancy text run around. Essentially they will be able to change content not style, but that should suffice.
2) This is more feasible: TOOLS>TYPEWRITER. Literally you can make/edit containing boxes that OVERLAY type in them. Again this goes ON TOP of the existing design and utilizes only included or system fonts. But technically you could do your design sans-text , save as PDF , edit the text in acrobat ( or leave the content for him to add, tho he will only be able to use the fonts he has).
Keep in mind, as Slackr has pointed out, that Acrobat is NOT a layout/editing application... so results will vary.
hope this was helpful