Short answer is YES. However, your cutting, water, process, location and light are important factors for your cuttings to root and I'm going to tell you exactly what to do:
WHAT YOU NEED TO PROPAGATE GERANIUM IN WATER:
- A razor, xacto or a sharp thin blade knife
- A geranium plant to get the cuttings from
- An empty jar
- If your Jar has a large opening, then you will need some tape
- & of course, Water!!!
To choose a perfect cutting you are looking for a green, young branch with few leaves and preferably two leaf nodes. If there are not leaf nodes visible, you want to have more than 4 leaves on the branch so that you have remove two leaves and expose the nodes. Leaf nodes are very important as that's where the roots will grow from. This might take a little search, and it is an important step, so take your time!
In the picture below, notice that there is already one leaf node on that branch and if I remove one leaf right above that node, I will have two leaf nodes and there will be few small leaves left so that my cutting can feed and stay strong.

Time to snip! Remove your chosen branch by cutting it close to the stem with your sharp razor in one cut. Then it clean it up by removing any flower buds or extra leaves, cause you want all the energy to go toward growing roots and not the extra leaves, also any flower buds will most likely die and rot, so remove those too.
HOW TO PROPAGATE GERANIUM IN WATER:
Now that your cutting is ready, fill up your jar with water, and insert your cutting in the water, in a way that the two leaf nodes are in the water & the leaves are out, look at the picture below.
Keep the jar close to a window at room temperature. You want, maybe, a north face window or somewhere with lots of bright light but not direct sunlight.
Check your cuttings every few days and add water to the jar if water level has gone down.
A few tips:
- If you have a large opening jar, make sure to cover most of the opening with tape (or yarn) then insert the geranium cutting through a small opening in the tape. This is to prevent your cutting from sinking in the water too much, otherwise the leaves will start to rot & that will be the end of it.
- I suggest not using water straight from the tap; fill up a cup/container with water and let it sit few hours to get rid of any chlorine in the water.
- Those little white spots from a fallen leaves or the tiny white leafy flaps are your clue for where the leaf nodes are.
Picture below shows you why having leaf nodes are important. The jar on the right is without leaf nodes, and see what happens in few days!.

After 15 days:

HOW LONG FOR GERANIUM CUTTINGS TO ROOT IN WATER:
Roots will show up after 2-3 weeks, mine took 15 days and you can see the roots starting to peek through. A side note that I didn't use any rooting hormones or cloning gel.
& There you have it :)
Hope you enjoyed this guide & Please let me know if you have any questions or do share your thoughts if you gave this a try.
Cheers,