Does size of one particular column in a database affect query performance?
A short answer would be: Yes, it affects performance.

A database stores it's data inside formatted database blocks. These blocks are the basis of all caching mechanism, so caches will store database blocks. Querying the database will move some read blocks into the query cache.

You can imagine, the smaller a block is, the more blocks can stay safely inside the caches without having to drop them for new blocks from new queries.

However, I'd say that in many scenarios that store data this way, performance differences of the kind I described might not be the most prominent factor for the underlying system. A benchmark might find differences, but for a system to react noticeably faster you need at least 10% faster responses (the number differs from study to study), and I'm not certain excluding the text column to it's own table will give you that.

On the other hand, if the column would be indexed, that might make matters different. But as I see no index other than the primary key, I see no reason to refactor here - other than that such a column is considered bad practice.