Q: can i connect airport time capsule wireless to my existing network

Unfortunately, the Time Capsule was not designed for the type of installation that you are asking about. It really needs to connect to your existing router using an Ethernet cable....as you see illustrated in the Setup Guide that came with the Time Capsule.

It is not recommended, but might be possible to configure the TC to connect to the existing wireless network using wireless only......but even if this works.....you will have to put up with a very slow "double hop" wireless situation. You can skip the next three short paragraphs to save time if you already know about the downsides of a double hop wireless setup.

Double hop occurs when a computer that is backing up has to send the signal back to the main network router over wireless.......hop one......and then the main network router has to send the signal back out to the Time Capsule over wireless.....hop two.

So, the normal time that it will take for a backup to occur over wireless will be doubled....and....the chances of an error occurring during the process will be doubled as well.

The initial Time Machine backup.....when the entire Mac is backed up....will probably take a day or two for each Mac.

Simply stated, I would never do this.

But, if you want to try, we can tell you "how" to try. What we cannot tell you is whether it will work.....or, if it works, how well it might work for your purposes.