I've seen variations on this question come up a few times, it can be basically summed up as "If I do {uncommon thing} with my password will it make it stronger?" whether that is adding alt codes, using non-ascii characters, typing it twice, whatever.
The assumption generally seems to be that if you do something password crackers are not expecting it will increase it's strength. Which sounds reasonable on the face of it, but it's the wrong way of looking at password strength. What you should be looking at is the amount of entropy in your password (that is, how large is the pool of possible passwords from which that one was selected?), rather than how that entropy is displayed.
For example if you used dd if=/dev/random count=18 bs=1 2>/dev/null | base64
that would get 144 random bits of information, and output it as base64 it would be displayed as 24 characters, but if you used dd if=/dev/random count=18 bs=1 2>/dev/null | xxd -p
thats going to output the 144 bit as hex, so it will be displayed as 36 characters. But they are both the same strength.
So to answer your question: No, using alt codes does not in and of itself increase strength. To increase strength you need more entropy (a larger pool of possible passwords). But it dose reduce the number of characters you need to store that entropy. So if you were using a service that limited you to 16 character passwords (Hi Microsoft Live) it could be useful.
This is the short version of a longer rant I did that a few weeks ago.