The wireless internet over mobile cellphone networks is basically the same as voice calls except for networks like ATT which have separate 2G & 3G networks for the most part. Typically the 2G (GSM/Edge) network will handle only voice and some data services for 2G-only devices. ATT will also handle voice over the 3G network. Usually, there will be both technologies at each location. Verizon's network evolution is along a different path where the lines between 2G and 3G are not as sharp as the two different technologies that ATT uses. The difference between data and voice on all the carriers will be similar in similar situations. All voice calls over wireless networks are in the form of digital data. It may not truly be voice over IP yet, but still is subject to the same limitations as your traditional internet service. High speed 3G data (internet) over radio is subject to signal fluctuations, low signal strength, interference, etc. All of this affects the error rate which directly affects the data speed. This is why it works better in good signal areas than poor one's.
All carriers don't have their latest and greatest network enhancements everywhere either. Sprint may only offer limited data rates or limited rates due to factors outside of their control. I'm not familiar with Catalina Island but being an island more than a few miles off shore, backhaul ( the link back to Sprint's network) could be severely limited and incredibly expensive. That would be a bottleneck for data.
Your amplifier may be a solution, but if the tower you are trying to communicate is on the other side of a mountain, you're probably still SOL. If you're getting a weak signal, it should be an improvement. Ideally, you would get what is called a bi-directional amplifier. It receives a signal at an antenna mounted in an ideal location, such as on your mast or a spreader, then routes it to the amplifier which then sends it to an antenna inside your cabin. The opposite happens to transmissions from your cell phone or aircard. It's not so much that the signal out is amplified, but the signal is routed to a superior antenna in a far superior location. The amplifiers are specifc to certain bands and there are some dual band models that cover all cellular and PCS bands. That would be the ideal way to go, but may require separate antennas for each band. The drawback would be with the rollout of 4G service from all of the carriers. ATT & Vz are going to utilize the 700 MHz band for 4G data. This is great for improved performance, rf wise, over 3G, but I haven't seen any 4G compatable bi-directional amplifiers that work on those cell/PCS & 700 MHz. I'm not really sure the of frequencies used for WiMax by Sprint. They could have special restrictions on an island too.
Before you bite the bullet, you should call them and ask specifically about frequency bands used on Catalina Island. You should ask to speak with someone in their RF ( Radio Frequency) Engineering department there locally and explain exactly what you want. They should be helpful in suggesting the best devices to use and should have fairly accurate coverage maps of the area. One bad thing ( just my opinion) with Sprint is that they farm their engineering and maintenance out to another company that may not have customer service at the top of their list like Sprint employees would. You might be pleasantly surprised at the lengths they will go to help you.