Can I search the URL fields in the indexed documents?

Yes, you can search URL fields, however, it is a bit different than searching content and other fields.

For example, if you index http://searchblox.zendesk.com, and you need to search the domain, you must provide the search term as follows:

url:searchblox.zendesk.com
or
url:*zendesk*

The parent URL between http:// and / would be taken as a single term. 

You can also give the full URL with special characters by enclosing the URL within double quotes:

url:"http://searchblox.zendesk.com"

Sub-paths can also be searched directly. For example, if you need to find whether the word "searching" is available in the subpaths

eg: http://searchblox.zendesk.com/Searching/8493930

the query should be:

url:searching

You can also combine queries using logical operators along with URL parameters as:

collection AND url: searching

To learn more on fielded searches read: Fielded Search in SearchBlox