From my personal point of view a merge of the two projects into a crossover is rather unlikely. (At least, I hope so! otherwise they will have a big problem with the fanbase...)
/controversial discourse start/
Well, I don't want to be off-topic but, for some reasons, Burst can be already considered something close to a failure
(take this statement with caution, I am not actually saying that it is already a failure), even if they could sell quite regularly in Japan.
For example:
-Out of Japan they don't have the same "commercial strenght" of their predecessor. This is quite easy to explain. Bakuten Shoot progressively led to the construction of a solid fanbase globally and the Metal Fight had a big bump partly because of the big Bakuten Shoot fanbase return, Burst instead hasn't had such a boost or at least not so big.
-They are something that for many purists is difficult to call beyblades, so they are not interested in them.
-The anime/manga changed its connotations too much, not everyone like this.
Anyway every brand has changes during its lifetime, we have to face it.
Evaluating the numbers we can't actually mark it as a failure, but for other aspects it could be considered a failure in a future global optics (compared to Bakuten Shoot and Metal Fight). This kind of analysis are always better if considered in a long term period instead of a restricted time window, and morover on a larger scale than just Japan, the same goes with Rising, obviously.
Rising isn't a failure, it is just...Rising lol whatever it is.
I know that reading "Bakuten Shoot" before "Beyblade Rising" is like putting a knife straight in the heart but...people needs to perceive this kind of things less seriously, it needs to be considered just as something celebrative, not a new start point for Bakuten Shoot.
/controversial discourse end/
So, anyway, returning in-topic, a crossover could still be an unlucky possibility if they see that is necessary. IMHO I think that a crossover to gain more popularity and increase the user base could work in Japan but outside...I don't know, I think that would be less effective, they have a different culture and a different mental conformation/approach to anime and manga. They can't repeat the Metal Fight global boost again, are totally different cases.
These are just my opinions, don't kill me guys.