Folder C:\Documents and Settings\[...]\Local Settings\Application Data\Adobe\Acrobat\7.0\Cache\Search70 contains lots of .IDX files, not too much, just a few MB. I am just wondering what these are, and if CCleaner can take care of these?

I have Adobe Reader 7.0 disabled in CCleaner because I want to keep the Recent Documents list. If I enable it, will that also erase my Adobe Reader's Recent Documents (as well as the data in the mentioned folder)?

I just looked at winapp.ini and the files you mentioned are removed by CCleaner already so yes if you enable cleaning of adobe 7 it will remove them but as you said it will also remove your mru list.

Below i have simply removed the mru cleaning in Adobe but it will still remove everything else including the files you mentioned. Simply copy the below to your winapp2.ini file which is in your CCleaner installation directory. Hope it helps.

[Adobe Acrobat Reader 7.0]
LangSecRef=3021
Detect=HKCU\Software\Adobe\Acrobat Reader\7.0\AVGeneral
Default=True
FileKey1=%userprofile%\Local Settings\Application Data\Adobe\Acrobat\7.0\Cache\Search70|*.*
FileKey2=%ProgramFiles%\Adobe\Acrobat 7.0\Reader|*.bak
FileKey3=%ProgramFiles%\Adobe\Acrobat 7.0\ActiveX|*.bak
FileKey4=%ProgramFiles%\Adobe\Acrobat 7.0\Reader\plug_ins|*.bak
FileKey5=%ProgramFiles%\Adobe\Acrobat 7.0\Reader\Updater|*.bak

Thank you for your advice. But I'm sorry, it's not 100% clear.

I do have a winapp.ini file, but no winapp2.ini file. Do I create it with the data you suggested in it?

Have a look here:
http://forum.CCleaner.com/index.php?showtopic=1110

You can either create one yourself or you can download the zip file at the bottom of that link. It will also add a couple of more programs to be cleaned if you have them installed.

Sorry about not explaining that you have to make one. Just download this file and place it in your CCleaner installation directory