Depends on how you define "Notification." If you simply mean the same as getting notified for VMs, PMs, Rep, Friend Requests and Quotes, then the answer is no, however as you may know, you can subscribe to your thread and either choose "instant notification by email," "daily notification by email," "weekly notification by email," or "notification through Control Panel," by clicking the "thread tools" option while displaying your thread and choosing "subscribe to thread."
If you choose the instant email option and have email connected to your phone like most people these days, you will get notified whenever someone new posts in your thread. It's not recommended though if the thread and topic at hand is the type of thread that will receive 200 plus posts (since 200 plus emails a day is not good, lol). Easiest and best thing to do if you ask me is to pick the notify through (User) CP option, that way you can see whether your thread has a new post or not simply by heading to your Control Panel as mentioned above.
Also, you can find anything like new VMs and PMs, Latest Reps, Friend Requests and Quotes in your "User CP (Control Panel)." I don't remember using "My Base" for anything these past 7 years...
Hope that is good enough of an answer for you ^_^