Can I output 1080p at 240hz from my 2017 MacBook Pro 13inch with Touch Bar
Unfortunately, no.

Because your MacBook only has USB-C Thunderbolt, you will need a USB-C Thunderbolt to DisplayPort adapter. This Apple USB-C to DisplayPort adapter states that it can provide up to 60hz. This Apple article covers connecting UHD monitors with your Mac and states (paraphrased):


  The MacBook Pro (2016 and later) can support these resolutions and refresh rates over HDMI 1.4b when using the USB-C Digital AV Multiport Adapter with macOS Sierra 10.12 or later:
  Up to 1080p at 60Hz
  3840 x 2160 at 30Hz


Allan is correct, you will probably want an active Thunderbolt to Displayport adapter. I forget USB-C and Thunderbolt are not interchangeable terms.