When I do a search via Instant Search, does Outlook then also search for the text within attachments such as pdf-files?
Yes and no. While Instant Search does search within attachments, it cannot read all file types by default. In order for Instant Search to be able to search within an attachment, an iFilter for that file type needs to be installed. Instant Search is based on Windows Desktop Search which can already index over 200 common file types by default.
iFilter for pdf-files
While the pdf-format is listed, without an iFilter for pdf-files, Windows Desktop Search only indexes the file name for this file type (most other file types in the list are fully indexed though).
If you are using a 32-bit version of Windows and have Adobe Reader or Adobe Acrobat installed, then you already have a proper iFilter installed and pdf-files are being indexed so you can also search within them with Instant Search.
If you are using a 64-bit version of Windows then, aside from installing Adobe Reader or Adobe Acrobat, you must also install this 64-bit iFilter for pdf-files. After installing the iFilter, the Indexer will begin to rescan your pdf-file and index the entire text instead of just the file name.
Depending on the amount of files on your disk, this indexing could take a while though so Instant Search will not directly start producing results after installing the iFilter. Leaving your computer running with Outlook open overnight should get the job done in most cases though.
If you need full text indexing support for another file type, then you can find several more iFilters here. The list does look a bit outdated to me though so in case you need an iFilter for a specific file type, it is best to contact the vendor of the application that creates those files and ask them for a proper iFilter instead.
Note: If a (pdf-)file only contains images of text (for instance a scanned document) and no OCR has been applied, then there is no actual text in the document which the iFilter can index.