Does the command still have an effect despite the warning about stats not collected for your TEXT columns? Yes. Stats are still collected for the other columns in the table, and these will be available to the optimiser to improve your query plans.
Does the command have an effect at all on FULLTEXT indexes? Probably not on your FULLTEXT indexes since they are presumably on those TEXT columns whose stats were not collected. If they were created on VARCHAR or CHAR columns instead, then maybe stats could be collected, and theoretically that could help the optimiser.
Be aware that the purpose of collecting the table stats is simply to help the optimiser create better query plans. It doesn't do anything to the indexes themselves to speed up queries. Better query plans means things like choosing the best index if there are multiple to choose from, or maybe in some cases omitting an index that isn't helpful. And to choose the optimal join order of the tables.
If you don't have a particularly complicated query, then it's perhaps not surprising that collecting the table stats didn't improve your query's performance. You can check what your query plan looks like using the EXPLAIN <query> statement (doesn't actually execute the query) or ANALYZE <query> statement (does execute the query which can be helpful as it gives some more interesting output).
