That's the theory. But, because you are sending a very small electrical signal over very high voltage AC powerlines, and the signals must travel all the way back to the main AC circuit box, things do not always work as well as the theory suggests. So, the bottom line with these devices is that you will not know how well they might work in your home.....until you try them out in your home. So, if you decide to try these adapters, it would be a good idea to understand the store's return policy in case the adapters do not perform well for you.
An Ethernet cable connecting the two wireless access points would always be the best way to go in terms of reliability and performance.
Trying to connect two wireless access points wirelessly is always the last choice in terms of performance, since so much of the signal is lost in this type of process......but it can work if the "extending" device is located where it can receive a strong wireless signal from your "main" router.
Regarding your Linksys, as LaPastenague mentions, we know nothing about this device. It might be a modem/router, combining both a modem and router in one package. The Time Capsule does not have a modem on board, so if the Linksys really is a modem/router and you replace it with a Time Capsule, you will need a separate modem for the Time Capsule if you want to be able to access the Internet.
We could give you a better answer about things if we knew what model of Linksys that you had. We don't need or want the serial number......just the model number.