I think that's part of it. Also, probably has an NFC reader for Amiibo (assuming they are keeping Amiibo support), and judging by the light indicators on the left and right, it charges the joy-cons. (The lights indicate battery level). Speculation as always, but that seems to make more sense than having two sets of lights for a player indicator, which is the only other purpose I could think of.
Back to the original question... I highly doubt they will add Wiimote support. The Wii remote was designed for motion controls and for pointing at things on the screen... Neither of those work for mobile gaming. Of course, it could technically be relegated as a "normal" controller and just drop the functions that make the Wii remote unique. Also note that each joy-con has a joystick, 4 buttons in a diamond shape, and 2 additional buttons. The Wiimote's layout is not really conducive to this, plus it only has 5 buttons (since the power button is not really a usable button in terms of gameplay.)
What I think is a little more likely is for the Wii U Pro controller to be compatible, not least of which because it was for Wii U and not Wii. However, given the name change, it seems plausible that Nintendo wants to wash their hands of the Wii brand and not confuse consumers by having Wii accessories for the Switch console. (This would be a source of confusion for a lot of adults who are not into gaming, even if it may be an easy concept for you or I to grasp.) On top of that, we see a glimpse of Switch "Pro Controller" during the Splatoon fight in the trailer. Why would they make a new controller that is practically identical to another compatible controller? The answer is... that other controller isn't compatible. You need a Switch controller for the Switch system, period. Also note that this controller features the mysterious square button which also appears on the left-joycon, and the Wii U Pro controller has no equivalent.
With the Wii U Pro and the Wiimote out of the picture... I think it's pretty safe to assume they will not give the Wii U gamepad compatibility either. It wouldn't make any sense anyway, because it requires a specialized video transmission from the system, and it's paired to your Wii U, intentionally designed in such a way that it cannot be easily de-paired and paired with another system.