Can I use an old Time Capsule as an external drive by connecting it to a Mac?

There are two options to set up the old Time Capsule to do what you ask.

1) Set up the old Time Capsule to wirelessly "extend" the new Time Capsule, and then connect your Mac to one of the three LAN ports on the old Time Capsule using an Ethernet cable of the length that you need. Your Mac could also connect to the old Time Capsule using a wireless connection if that would be more convenient.

2) Connect the old Time Capsule to the new Time Capsule using a permanent wired Ethernet cable connection, and then use another Ethernet cable to connect your Mac to the old Time Capsule. Like option 1) above, your Mac could also connect using wireless if that is more convenient.

I have two Apple Time Capsules ethernet connected in my local network. One upstairs and one downstairs for the wife's Mac. She uses the older TC to save all her files. We don't use Time Machine. The second Time Capsule must be placed in bridge mode. Do that using Airport Utility. The second Time Capsule is also set up with its own wireless network so she can use it for her AppleTV.