Yes they would. Obito told Kakashi that the kamui wouldn't work on him after Sasuke's fight with Danzo; and his eye's ability is similar to Kakashi's. He continued wearing a mask even after claiming to be Madara. Additionally, his physique and mobility is far superior to that of an 80+ year old man. Not even Mito (strong life and vitality) could keep up such a youthful appearance, so even with Senju DNA, it's unlikely Madara's could (and he didn't). So now they have an eye technique that resembles Kakashi's and a seemingly youthful body (compared to a would be 80 year old man), and even more the statement from Obito "That won't work on me." Of course, there's always the possibility that teleportation techniques shares the same dimension, but they have three (or was it four?) shinobi that is capable of utilizing the FTG. I can see them experimenting with that and Kakashi's kamui. After they inquire about Rin's death (if they didn't already know), they'll find out that Kakashi killed Rin; and Kakashi's promise to keep her safe. It's a motive to consider. As for Obito's pretense as Madara, even Tsunade realized the power in a name. Obito's surviving the boulder incident may be puzzling, but so would Madara's survival.
After collaborating with the hokage and doing some research, they may have even got the idea to have Kakashi read the Uchiha Tablet with his mangekyou (I wonder if this would work), which most likely reveals on how to obtain the rinnegan, info on the god tree, the sage etc. They will probably begin to suspect that Madara fought Hashirama to obtain this (Kabuto and Oro also came to suspect this even without reading the tablet). And they would know exactly the true goal of akatsuki.
The details of all Rikudou's jutsu is probably written on there as well, but more importantly, the Seventh Path. It has the ability to revive the dead. I wouldn't be surprised if they started picking apart Madara's plan from there.
I think at the very least, they would have always considered Obito as a possibility, and knew without a doubt once Obito started preaching to Kakashi (if they didn't circumvent his plans before then). Also, referring back to Obito's survival, it seems it was known that Hashirama was an excellent healer, after suspecting that Madara lived on through such means, it's not absurd to believe Obito did the same. Furthermore, the tablet speaks of traumatic experiences unlocking the MS (in the form of murdering a sibling), and Obito's 'disappearing' act is very convenient for such as that boulder occasion. It's almost like it was made for that lol.
Let's not forget that Kabuto and Oro managed to figure out a lot.
So yeah, there would definitely be lots of clues and methods at their fingertips.