It depends on what you want out of the course.
If it's just a certificate or diploma you want, then online gem identification courses will give you a basic knowledge and a piece of paper. If you want to be truly adept at practical gem identification, then perhaps not.
I work for a gemological institute in Bangkok and I've seen many students pass their diplomas despite skipping class and practical sessions. However, when they are put to the real test - i.e. when they have to identify a gemstone in the field or out in the market - they fail miserably.
Bottomline is - you need to log many, many hours of actual gemological practice in order to be able to identify gemstones accurately.
Some issues to consider:
* How many hours of hands on gem identification practise does the online course offer? How does it compare with an on-location program?
* How large is their gemstone collection? How accessible are they to you for practise?
* Will you have access to their facilities (e.g. library, student lab) after you complete the course?
* Does the school offer other courses to complement the course you plan to take? Are there supplementary courses? Refresher coures? Regular updates on new gemological information? Seminars etc?
Hope that helps! Drop me a message if you want to find out more.
Personal experience. I teach at a gemological institute.