Creating a interactive sign up list in ONE cell

A drop down really won't work this way.  You could back it up with a macro but a) macros (VBA) are not supported in excel online and a number of other formats and blocked by default on most computers, and b) if you are going to use VBA I would go with a custom form or something anyway.

Alternatively, you can use a script and link that script to a button that will work in excel online and desktop and such.  That script can add the login name to the cell but that will be based on whose account is logged in on the computer, which may or may not be the actual person/email/info you want captured.  Another option with a script is to add a cell they can edit to enter their name and then the button just appends that cell info to the list you want.

Another alternative if you have the list of all invitees is to list them in columns to the right and then add a drop down below each for status like 'no response yet', 'yes', 'no', 'maybe', etc...  It would be hard to lock the sheet to prevent them from editting others but is that a big concern?  if on sharepoint you can review changes to see who made what changes.