I use (and love) Remember the Milk for a similar workflow (along with many others). The free account tier should cover your use case; the $25/year Pro version basically adds push sync to their mobile app(s). The main difference is that rather that notes and appending text to them, I use lists and/or tags and add items to the list.
Each account (I am alerque) is issued a special email address to receive incoming tasks. See RTM's help page for details. For example I can send an email like this:
Subject: The King's speech #movies
This will add a task tagged movies (or to a list named movies if I have on.
But there's more. Besides adding an item, you can also give it more details including a full length description in the body of the email. Ar say the movie hasn't come out yet?
Subject: The Hobbit, The Battle of The Five Armies #movies ^Dec 17
Now this won't show up in my movies list until it comes out.
If you don't like this abbreviated syntax, you can use more natural language (e.g. "on date" instead of "^date". See SmartAdd for details. You can also use a more verbose template format in the email body. Additional meta data can be provided as either known fields like URL, location, reminders, etc. or in a free form text field.
Besides email, you can use Twitter DM, mobile apps and various extensions to add tasks using the same syntax.
The results are not only searchable, but smart-lists allow you to organize lists based on pre-defined search criteria.