Mapping signatures to aliases in Mail.app
In a word, no . . .

Unless you can create each alias as a separate account (as suggested in a comment to the OP,) Mail.app won't be able to apply a unique signature to them respectively.

That being said, and if you don't want to create distinct accounts in Mail, you might consider using the text expansion feature of OS X.


First, open the Mail app and copy your desired signature into the clipboard.  Then remove it from the account
Open System Preferences / Keyboard
Select the Text panel  


  


Click on the '+' at the bottom of the list of shortcuts
Type a short, uncommon string for use as your signature shortcut in the Replace column.  For example:  


&amp;sig1


Tab into the With column and paste your signature text there
Tab out and your shortcut will be active
Repeat for any additional signatures you'd like to use.


Then, at the bottom of your emails, just type the shortcut text ('&amp;sig1' in this example) followed by a space, and your signature will appear in place of the shortcut text.  

While it is not ideal, it IS far simpler than changing your default signature in Mail every time you use a different account alias AND you may find the text expansion feature useful in many other situations as well.