no a brita would not even be close to the same results.
it just depends on your kitchen faucet. there are adapters that can thread into the faucet, but a kitchen sink is not deep enough for the filter as it's about 10in or 12 in. long. a washtub faucet in a basement would be easy to install the filter onto if you have a basement.
depending on grocery stores you have around, you can get filtered water on the cheap from them if they have a "fill yourself" station for water. and depending on how many plants you're planning on running, this may or may not be convenient.
or another option is buying an RO filter system, which are relatively inexpensive these days. i think the grow store by me offers one for around 125$. then all you have to do is tap a line into the cold water line under your sink cabinet.