Can the catalytic converter be clogged with no power loss?

Catalytic converters can go bad without clogging and if it is melted, it is due to overheating mostly due to excessive fuel getting to it, a misfiring conditin. If problem was before replacement of engine, it wcould be the engine fault but if it is still overheating, glowing red hot after some driving, you need to ensure there are no misfiring or excessive fuel getting to the catalytic converter.

I think the issue is the terminology that you are using. A "clog" by definition would be something that definitely would effect performance but there are many ways a Converter can be damaged/faulty and require replacement without actually being clogged. As KHLow2008 pointed out, there is likely an underlying cause of the damage that needs to be found.