A similar discussion is happening in another thread on the forum right now. @AMosca96, I recommend taking a look at this post.
The approach you're describing will not resolve the ASVs from the two different runs into the same ASV as, if I understand the approach correctly, the ASV ids are not going to be updated post trimming of the sequences, so you will continue to observe them as different features in the merged table (which will lead to an apparent batch effect that is bigger than what is probably there). There are ways you might be able to post-process those data to address this - eg., de novo OTU picking at 100% identity following your trimming and merging, but I wouldn't recommend this route. Rather I would go with one of the approaches that are covered in the post I'm linking to.
Note there in all realistic scenarios, there will always be a batch effect if you're using different primers, because the primers are enabling you to "see" different community members due to primer bias. Combining data sequenced with different primers is therefore always an exercise in trying to manage the bias that we know is there.