Are egg-whites acidic?
Sounds like a good experiment. My answer would be no.
You have the relevant reaction chemistry. This sounds like an excellent A level laboratory experiment. Remember to introduce a control, as atmospheric carbon dioxide will always be in equilibrium with dissolved carbon dioxide.
Note that most things that taste good (Coke, though I much prefer Chinotto, milk, cheese, yoghurt, wine etc.) are slightly acidic. Things that are slightly basic, bicarbonate of soda, or egg white, tend to be quite bitter and not flavorsome.