Not really*. An automatic weapon on modern kind needs standardisation, which was taken into use around American civil war. You see the automatic rifle needs precision parts to produce consistent results.

Standardisation is much harder than youd think. See medieval manufacturers didnt have access to precision lathes, even of the kind Elisebathian englad had to use (which is why manholes are round since that was the only manufacturing method that was precise/cheap enough to fit them at the time). So first youd have to use a precicion lathe that makes standard componenets to make a precision lathe that makes standard components to build a precission lathe. And offcourse youd use this lathe to make cartridges that fit your barrel each and every time.

So first you would need to retool the entire manufacturing industry, break guilds etc. See medieval system was based on artisan skills. Handworking is their core, the guilds might not look too favorably of demolishing or at least marginalizing them. This would also be somewhat in contradiction to the world view of most of the population.

Then you would need to advance their metallurgy so that they could make steel suitable for the job. Manly so you could make tool bits for your precision lathes. etc.

\* on the otherhand you could make something like the repeating crossbows of china, does that count?