I can't speak specifically about furniture polish. However, when putting a substance on a chain to lubricate and/or clean it, be careful. Something that seems ok in the short run may be harmful in the long run. (For example, using acetone to clean a chain may work in the short term, but it can displace oil inside the rollers, leading to dry chain problems later on.)
There are some chemical products that you don't need from a bicycle shop. For example, when cleaning out hydrapacks, you're better off using bleach rather than the hydrapack cleaning solutions. However, buying some bicycle lubrication is not a bad investment.