I am taking a free music production course that was told to me by another member. In it they suggest that I record using 24 bit, but my audio interface (alesis multimix x 4) will only record in 16 bit. My question is - Can I turn the 16 bit into a 24 bit once it is in my DAW, and will it still be useful? 

Yes and No,
the benefit of increasing the bit rate in sonar/Music Creator will only be that you will have some extra space to mix with, but that benefit is small in comparison to recording AT 24bit.
 
The benefits that they will be talking about in that class cannot be reached by an increase in bit rate after the soundcard's converters have already converted analog to digital at a specific bit rate (in this case 16 bit).  you will gain a HUGE benefit if you purchase a soundcard capable of 24bit recording.

OK, Thank you.