It shouldn't, there are plenty of people who can go into extreme altissimo ranges on a student sax.  I'd be more concerned about whether working on altissimo is really worth my time, if I were you.  Sure it's good to know, but theres a world of things to learn in the natural range which might be more benefical to your playing.

You absolutely can do overtones on a student model saxophone. In fact, they generally speak fairly well on a Yamaha 23 alto.

Blowing overtones is not only a great exercise for developing your altisimo register, but its great for developing a good tone and for learning control of the instrument. Almost nothing teaches you proper embouchure, support, and airstream control like blowing overtones. I recommend overtone exercises for anyone who's mature enough to do practice it correctly. Also, check out Dave Liebman's book, "Developing a Personal Saxophone Sound".

Cheers,

     Mark Overton

     saxquest.com

Yes  .. . . .you can can on a Yamaha 23.

Here are a few tricks that may help you:

1. Start by playing the first overtone octave on Bb and hold that pitch for a whole note. Then play a chromatic scale one note at a time on the overtone in that partial until you lose the sound. Focus your attention on the notes around the probelm until you can get throught them all. More than likely you will lose it around E, but it will come with practice.
2. Follow this up with the second Partial and repeat.
3. After doing this, play a Bb Flat Scale on the first partial with following fingerings. Low Bb, Low C, Low D, Low Eb and then go down to the low Bb again to play the F, Low C, Low D, and then the Low Bb again. Inother words you only play the first four fingerings and then play the remiaing notes of the scale as overtones.

Hope this helps. Dave Liebman is amazing. I would also look into the Top Tones book by Rascher.

Good Times and Happy Playing .  . . ..