Not exactly....what I am saying is that there is very likely to be a problem with the cam phaser. This is not the camshaft itself, but the gear that goes on the end of the camshaft and allows for variable cam timing. it may be a problem with the cam phaser itself, the control solenoid for the cam phaser, or possibly the electrical circuits that control the control solenoid. This is simply an EDUCATED GUESS, based on the information you have provided. To find out what actually needs to be fixed, you must first DIAGNOSE the problem....that cannot be done over the internet.
Anyway, the possible cam phaser issue would be the CAUSE of your problems. The catalytic converter getting clogged up would be the RESULT of the problem that CAUSED it....I hope you are following this....
In any case, this does not sound like a cheap fix. You should prepare for the worst. Catalytic converters are never "inexpensive". That is the whole reason the Check Engine light was invented.....to get your attention so you will get your vehicle diagnosed and repaired BEFORE the catalyst gets destroyed by some other simple malfunction. It has been my experience that 90% of the catalytic converters that get totally clogged up are the result of vehicle owners that continue to operate their vehicles with the Check Engine light on, and don't bother taking it to get diagnosed until the engine is refusing to run any more. By that time, the high-dollar damage has been done. This may not be true in your case, but if it is not, you are among the other 10%.....sometimes the catalyst just breaks apart inside and clogs things up for no apparent reason.....manufacturing defect???
COST is something else that cannot possibly be estimated with any accuracy before the problem is actually diagnosed. From what I can tell here, the catalytic converter being clogged up is almost a given, from the description of the problem that you have provided. However, there are MANY variables here that have to be factored into the actual cost of repairs. First, shop labor rates can vary greatly from shop-to-shop. Then the price of the catalyst itself can vary greatly, depending on if an original equipment type catalyst is used, or if a cheap "universal" catalyst is used.
Anyway, if you need an estimate of the cost of the repair, I highly recommend that you get that from whomever you are considering for the job. Anything I can tell you over the internet would be pure speculation and probably very inaccurate at best.