older airport extreme base station as a network extender with new time capsule

Yes, although it maybe disappointing..

There are two kinds of extending.. wireless repeater type which is poorest as it has to transfer all packets in two steps instead of one.. hence will halve the speed.

Or using ethernet to the old extreme and set it in bridge.. You can then setup roaming network... this is much better.. but getting ethernet to the right place could be messy or expensive or both.

http://support.apple.com/kb/HT4260

wireless extend doco.. mind all of this is out of date.. the basics are correct.. the methods via the airport utility may be obsolete.

http://support.apple.com/kb/HT4145

Documentation has rather lagged lately.