Will it run smoothly?

It should run the entire game about as well as any laptop can and Asus makes high quality builds even on the lower end of their range like this one. The one drawback I see is the 256 GB SSD, more for sanity reasons. It is possible to game on a drive that size but you will constantly be fighting to preserve enough free space to keep Windows and the game running properly, presumably by offloading content downloads and saved games to another kind of storage device.

If you can go just a little higher on price, this one has an SSD that is twice the size at 512 GB and an arguably stronger processor. Its graphics card is in the series that came before the one that the Asus has, but honestly TS3 isn't going to be able to tell the difference. I'm currently seeing it as only $30 more.
https://www.amazon.com/dp/B07TN4C9FY/ref=psdc_13896615011_t5_B07VBK4SYS

There could be other considerations to take into account if you have other uses in mind for this laptop or will do so in the future, such as games that are more demanding than TS3 can ever be.

I don't really have the savvy shopper gene though, and others may come along and make some slightly different suggestions still within or close to that price range. If you have time to look around though and can go higher, I would be more comfortable with 16 GB of RAM on a new machine, although usually RAM can be added later easily enough. The game can't use that much RAM, but it's a lot smoother to use other applications like web browsers alongside of it when there is that much to spare.