Does the sun now 'bypass" some of the original zodiac constellations?
The ecliptic still passes through the original 12 constellations, although Earth's precession has shifted the Sun's apparent position by roughly one constellation. That is, if your birthday is today, May 2, an astrologer would claim you were Taurus, whereas in reality the Sun is currently positioned in Aries.

Additionally, the ecliptic now passes through the constellation Ophiuchus (The Serpent Bearer). You can see the "historical" and the "true" constellations e.g. here.