I have an external SSD drive that connects via USB 3.0. If I use a USB 3.0 to USB-C adapter would I be able to take advantage of the faster USB-C speeds or would the transfer speed still be only as fast as what USB 3.0 would give me?
Your speed will be at USB 3.0 speeds.
When negotiating between slower and faster protocols, the transfer will only be as fast as the slowest side of the connection.
While USB C connections have the potential of reaching speeds of 5Gbps to 10Gbps when using USB 3.1 Gen 1 and Gen 2 connections, if you are connecting via USB 3.0 there is no guarantee you will reach speeds like that simply because you are connecting a USB 3.0 devices with a USB C adapter.
That said, USB 3.0 devices might be able to reach 5Gbps if it is a USB 3.0 SuperSpeed (SS) device. But it is not guaranteed.
For example, I had a Seagate Backup Plus 4TB USB 3.0 that I connected to the USB C port on my MacBook Air and the speed honestly wasn’t 5Gbps all time. I was able to improve the speed of the drive by removing it from the standard Seagate Backup Plus enclosure and putting it in a new USB C specific enclosure. Now I consistently get solid 5Gbps transfer speeds from that device.
Past any USB protocol specifics, speed between digital devices needs to be mutually assured on both sides of a connection.
- Phone Modems: A 300 baud modem connecting to a 1200 baud connection will only ever be 300 baud.
- Ethernet: An 10Mbps ethernet connection connecting to a 100Mbps device will only ever be a 10Mbps ethernet connection.
- And so on… And so on…
That said there might be improved USB 3.0 speeds depending on the device because newer devices tend to use newer/faster components. As I explain in my answer to this other SuperUser question, I saw a very clear improvement in speed when I connected external USB 2.0 hard drives to the USB 3.0 connection on a Mac mini.
So in the end nothing is guaranteed as far as actually speed of a slower protocol goes, but no matter what speed you get it will never be faster than the slowest side of the equation.
Connecting a USB 3.0 (5Gbps, Gen1) device to Type-C port won't give you the Gen2 (10Gbps) rate, this should be obvious. The USB3.0 device will send "capability message" as Gen1 device, and the Type-C host will switch into Gen1 mode even if it might be Gen2 capable.
However, Gen2-class controllers usually have higher bandwidth on the side between USB (xHCI) controller and PC host data fabric/memory, and usually have some other enhancement to DMA tranfers (like prefetch). So the host-contorller overhead will be less, and your device might have slightly more efficient bus utilization and therefore slightly improved performance (likely only on some specific benchmark-style workloads), which you might be unable to notice in reality.