Ill try and make this quick, lets assume this is the sasuke before he fought danzo. Meaning has regained most of his chakra but also has enough experience with the ms.
Now jiraiya's base is slow. He cannot avoid amaterasu or a susano arrow. If he were to try going into sm by using the same strategy he did on pein (animal path) he wouldnt be successful. Not againbst somebody who has been shown to be able to control manda. Chances are jiraiya would summon one frog and if thats the case he can be controlled and used against him.
Lets say he summon more than 1. Lets say he summons 3. To keep sasuke busy. Depending on the size and quantity of your summonings that alone can take 1/2 of your chakra. Lets say after summoning 3 frogs he has 1/2 chakra left and he gets into sm. We all know that jiraiya for a start cannot balance sm properly thats why he partially transforms. We also know that sm suits people with high chakra levels to balance it out with natural energy. If jiraiya has used 1/2 of his chakra just to distract sasuke and get into sm, sooner or later the natural energy would overcome his chakra.
Lets not get ahead of ourselves though. Even with 3 summons they are vulnerable to many attacks, by sasuke.
Besides not only can pa and ma frog be controlled to gather more natural energy than needed, meaning jiraiya would turn to stone, even in sm his speed isnt on par with v2 raikage