yes you can do that but the question would be what method you want to use?
There are many ways to do what you ask or speak of.
If your programming your website in PHP then take a look at this:
Click Here
You can do this via php. If your having people to directly connect to your FTP server.
Then you can do this via a bash aka a shell script.
here is one:
Click Here
This just shows you how to code a bash script to interact with a FTP server.
Knowing this and then learning how to send e-mail via a bash or shell script.
You can do it that way or do it the C++ complex way.
yet what you talk about is possible. There are many many ways.
All you need to know is how to detect when someone logs in. Once detected then you must find out who logged in and their e-mail address and then send them an e-mail.
If your saying you want to be e-mailed. You can do it that way too. You may want to know who exactly logged in and at what time of the day. You have to grab that data and then e-mail the message to your e-mail account.
So what your saying is possible.