Your ex gf almost certainly will find out, and she will be hurt. So if you believe that hurting people is wrong, then yes. On the other hand, you can't live your life only trying to keep others happy. Shades of grey, Kiddo.
If this new fling looks like it is going to become a regular deal, you could do some damage control with the ex... Sit down with her and clearly tell her that the two of you won't be getting back together, and that you're seeing someone new. Explain that you're not telling her this to be hurtful, but rather that after what the 2 of you shared, you feel it is right to be honest, and that you want her to be able to move on.
And stop accepting gifts from the ex. That's kinda sleazy.
Good luck!