Welcome to the Raspberry Pi forums.
The easy bits with positive answers:
Can you interface to some sort of external cellular device and send an SMS/Text? Yes. (Or you might be able to find a 'gateway' on the Internet that would relay the SMS for you, possibly for a fee.)
Can you add an external Analogue-to-digital convertor to get external sounds converted into the digital form needed for further Digital Signal Processing? Yes. (But you will need to to some research to be sure that the resolution and data format are suitable for your requirement.)
The more difficult questions with no firm answers:
How do you know you are hearing a motorcycle? Is there anything common to the sound from a 50cc 'moped' and a 2l Harley? Do you have to catalogue the 'soundprint' of every known model and check each one? Does the sound vary during acceleration, cruising and braking?
Does an RPi have enough processing power to perform the analysis decided by the previous step in an acceptable timescale?
Good luck with your project.