There are 22 watt per channel tube amps and there are 22 watt per channel tube amps.
Generally (although not necessarily), the more expensive the tube amp, the more likely it is to have high-quality output transformers and hefty power supplies that will make its wattage rating less important (i.e., the amp will be more powerful than its wattage rating would otherwise suggest).
To respond to your question, if your Klipsch speakers do not drop below 6 ohms or so, and are anywhere near 102 db/watt sensitive, any decent 22 watt tube amp will make them go very loud. If you want a 22 watt tube amp that will drive less efficient speakers, however, then you have to be really careful about what you buy and, generally speaking, this means pulling out your wallet (top-shelf output transformers are very costly).
Generally (although not necessarily), the more expensive the tube amp, the more likely it is to have high-quality output transformers and hefty power supplies that will make its wattage rating less important (i.e., the amp will be more powerful than its wattage rating would otherwise suggest).
To respond to your question, if your Klipsch speakers do not drop below 6 ohms or so, and are anywhere near 102 db/watt sensitive, any decent 22 watt tube amp will make them go very loud. If you want a 22 watt tube amp that will drive less efficient speakers, however, then you have to be really careful about what you buy and, generally speaking, this means pulling out your wallet (top-shelf output transformers are very costly).