It's possible, but not straightforward. You convert the table of contents to a two column table using the tab as a delimiter. Next, you sort by Column 1, and then convert the table back to text again, using tab as a delimiter. The page links are maintained, but there is no hierarchical indentation. This simply produces a single alphabetized list. Once the table of contents is alphabetized, you need to select all the entries and insert a tab stop for the page numbers.
The challenge is the first step. You want each entry in the table of contents to be its own row in the table. One way to achieve this is to go to the first entry in the table, and replace the first letter with a space and the letter. Essentially, you want a space before the first character, but the space must be inside the shaded portion. Then when you select the table to convert it, you select starting from the bottom omitting the lone paragraph marker, and select everything except the leading space character you entered for the first character.
I wouldn't recommend doing this, unless your table of contents had lots of entries. For tables with just a few entries, it would be quicker to sort by cutting and pasting.