The short answer is...maybe.
If you have a handheld satellite phone (for example, an Iridium 9555, Iridium Extreme, Globalstar 1700, or Inmarsat IsatPhone Pro) then the answer is resoundingly no. There is simply no way that the bandwidth of those devices can handle even the most basic Skype requirements.
Which means you need to look at a broadband unit.
Skype states that the minimum data requirements for basic video calling is 128 kbps. Right off the bat, there are several broadband units that won't cut it for that requirement. An Iridium Pilot at 32 or 64 kbps is out of the picture, for example.
But an Iridium Pilot at 128 kbps, you might be thinking, will do the trick!
In fact, even Fleetbroadband 150, Fleetbroadband 250, and many of the lower-end BGAN units can't match the upload speed required.
The only broadband units that guarantee bi-directional upload and download speeds are the Fleetbroadband 500 and the BGAN 700. Not even VSATs guarantee bi-directional, but their bandwidth capabilities are so fast that it doesn't usually cause an issue with regards to Skype.
Keep in mind, also, that BGAN, FBB, and most VSAT systems use shared bandwidth. This means that if you're in, say, a marina during a boat race and a lot of other people are using their satellite devices, you will not be getting the full bandwidth of those networks.
This could drastically affect your Skype performance, even on a high-bandwidth system.
So it comes down to a handful of units to even get you started with Skype:
At the time of writing, a Fleetbroadband 500 is around $16,000, KVH Mini VSAT is around $15,000, BGAN 700 is around $5,800, and BGAN 9202 is around $3,000 (although note that we generally don't recommend BGANs for maritime use - they need a very stable environment to work properly). So you're looking at a high startup cost for equipment.
Let me say, very clearly, that "Free Calling Over Skype!" is very definitely not free over satellite.
Breaking that down into a per-minute charge puts the price of a simple video Skype call at 1 MB per minute of talk.
High quality video (500kbps) is 1.67 MB per minute of talk.
HD video calling (1.5 mbps) is 5 MB per minute of talk.
Now, it depends on what your airtime plan looks like. If you have a basic Fleetbroadband standard rate plan, one minute of normal video Skype will cost you $17.65. One minute of HD video calling will cost you $88.25. Notably, one minute of simple voice Skyping would cost you $1.70 per minute - much higher than a voice minute for that plan.
But let's assume you have a really ample airtime plan, where MBs are much cheaper. On a KVH Mini VSAT plan where MB overage is at about $0.99 a MB (note: this plan is probably already costing you upwards of $1,500 a month)...you're still paying $1 for one minute of regular Skype calling, and $5 for one minute of HD video.
Let's say you have an all-you-can-eat, unlimited airtime plan for your Fleetbroadband 500. Ah ha! You might be saying, here's where it doesn't matter how much each individual MB costs - I can use as much as I want!
I'll go ahead and burst your bubble (sorry!) - Skype is expressly forbidden in the terms and conditions for all the unlimited plans.
Skype is a P2P based program, which means that even if you are doing absolutely nothing at all on it, it could be using your bandwidth to facilitate calling and data transfers over the network. This is why even minimal estimates for bandwidth usage (and, therefore, cost) are just that - minimal. The algorithm that runs Skype (and other P2P software like BitTorrent, for example) is programed to make the most out of any bandwidth it can find - even your very expensive satellite data feed.
Well yes. Although there are a lot of barriers to entry, people do use Skype over satellite. We had a customer who climbed Mt. Everest recently and Skyped with his family using his BGAN 700. It can work, you just have to make sure that all your ducks are in a row (equipment, bandwidth, and awareness of cost) and then - go for it! We'll wave hello right back at you while you climb that mountain, sail that sea, and continue discovering the unknown.