You don't need on-site GPS to know the elevation profile of your hiking trip. You can* plan the trip at home. Any modern map application will be able to show you the elevation profile of your trip.
That being said, you should have GPS with you for other reasons as well as a map.
* Actually, I highly recommend this
As someone who wants to guide through the mountains, I would think you should have a GPS regardless. Just like you should have a radio, maps, food, water, a first aid kit, knife, etc. It's a necessary tool of the trade. If you need to call for a rescue, the precise coordinates from your GPS will make you very easy to find.
Should I buy a GPS?
Maybe (or rather probably yes), but you don't need one to estimate elevation gain or loss, and they may not be very accurate for this purpose. There are good reasons to buy a GPS; I use one mostly for fun (geolocating photos with a track), but a track can also be a life safer to retrace your steps if you get lost, and a dedicated GPS ...
Vertical difference to summit: If you are just interested in reaching a minimum, it is often sufficient to compute the difference between the start and the summit, e.g. start at 1000m summit at 1800m means at least 800m elevation gain. Given the fitness level that is expected of a guide, this should already be enough in most places
Vertical difference along ...