Some, sort of, and it depends on the details.
You can use whatever logic you want on the smart things side with the end result of turning on a virtual switch which is also a virtual sensor, and then you can use that virtual sensor changing state to trigger an Alexa routine. (Assuming that everything is working the way it supposed to, the new skill is much glitchier than the old one was.)
At that point, you can have the “that“/action in the routine be to speak a preselected “notification.“
All of that works fine, when it works.
For example, I can have opening the front door cause my echo devices to say “The front door is open.”
I can also combine it with a presence check to say “Michael is home.”
But echo speaks could work with variables, so that you could change what was said on the fly. You can’t do that with the new skill method. So I believe in echo speaks you could have just one rule and insert a different name depending on who had just arrived, where with the new skill method you have to set up one routine for each person.
You could certainly set up a voice notification for something like “the mail is here“ if you have a detectable sensor to act as the trigger. But you have to have one routine for each phrase you want to speak, you can’t change any part of it. And you are limited to a total of 99 routines altogether.
All of which is to say some people can get everything they want just with echo routines, assuming the smartthings skill doesn’t glitch. But you could definitely create more sophisticated logic with fewer total rules using echo speaks.