Many people are already doing what you're thinking of doing. If you are planning on importing the images into LrMobile on the iPad, and you'll not be able to upload them to the Adobe cloud, make sure you buy an iPad that has sufficient internal storage to hold all the inages you anticipate taking in the trip. Yes, an external drive for backup is also needed, and some users will take enough camera cards so that they don't have to be reused on the trip (so giving you another backup).
Culling to delete the unwanted images before starting the automatic upload to the cloud is a good idea (in fact, if you happen to have a connection when you import another large batch, you might want to temporarily pause syncing until you've culled).
When you get back home, images will obviously resume uploading from the iPad to the cloud. You do not need to install the Lightroom desktop app (even though it's included in your subscription), but to get the images into LrC you need to enable syncing in LrC (if you haven't already done that) and that will ensure that ALL images in your cloud account will automatically download into the Classic catalog (a full copy of the complete original is downloaded). Be aware, however, that may also include any images previously imported into any of the Lightroom apps but not yet synced down into Classic.
Before enabling sync in LrC you should visit the LrC Preferences>Lightroom Sync tab....there you will find the option to choose a different location for the downloaded images (the default is an obscure folder in an obscure location on your system drive), which you should consider changing. Additionally, you can also choose to have them downloaded into one of the standard date-based folder structures (rather that into a single folder). My own LrC folder structure is date-based, so I have the location for sync downloads set to my single parent folder, and have the same date structure selected, so all images synced from Lightroom always end up in my one folder structure.