Yes, the Etrex Legend should do what you want (assuming you have a suitable cable for connecting it to your computer).
Note for uploading/downloading anything you need some software that supports the Garmin serial protocol. eg Garmin MapSource would work for loading maps, routes, tracks. Or GPSBabel is a simpler option for loading routes/tracks.
And the serial interface can be rather slow.
You can load maps, but the memory is rather limited (8MB). So you can use OpenStreetMap, but you are limited in how big an area will fit. Most OSM Garmin maps use fairly large tiles (4MB or so), which would be annoying if you are close to a tile edge, and need several of them. An audax may span a number of different tiles. So it may be better to use maps with less details, and with smaller tiles, so you can just get the area you need.
Maybe try these OSM maps designed for the Garmin Fenix, which also has limited memory:
http://www.gmaptool.eu/en/content/maps-garmin-fenixAs above, you can load routes or tracks to follow. Note the Legend does not support autorouting, so it will just give you a straight line between points in a route. But this still can be useful. If you want the line to follow the roads more accurately, you can load a track (limited to 500 points).
And yes, it will record a track for where you have been. So you can download this into MapSource, then save as a GPX file, then upload that to Strava etc.