Yes, you should be able to use either the camera on a USB cable or a card reader to download (and erase) the JPEG files...
If you want to do more (load CHKD, make card bootable, format at FAT16, download RAW, or upload scripts)--it is possible you will need to use a card reader for some/all of these functions. The camera and Canon software are not setup to manage the additional files used with CHDK.
If the camera is on--it is drawing power... Because you are using the external viewer--plugging in the AV cables turns off the LCD back-light on the camera--reducing power usage by quite a bit (1/2 or more?)... You may will probably need to change the camera's power save/auto-off functions.
Get a good set of batteries (Sanyo Eneloops or other hybrid NiMH batters have very low self discharge, 80% capacity after 1 year of storage--unlike regular NiMH which, after some use, can be dead after a month of non-use).
You could also use non-rechargeable Lithium AA batteries (1.5 volt). Great for very cold or hot weather, light weight, and will power the camera the longest of any type.... However, they are not cheap to replace (something like $2 each). Or, lastly, buy/make an external battery pack.
-Bill