Can the client be harmed in any way, and how?
There are a number of settings in the standard RDP client that could be exploited for an attack on the client, if enabled. For example: shared folders, access to devices like printers, etc.
If you're remoting into a known compromised machine, you might want to disable as much as possible in the client's connection and sharing options before connecting.
It's also possible that in addition to the things that you intentionally shared, there could be vulnerabilities in the RDP client itself. Ensure you're patched and up-to-date, and treat the client machine as at-risk of infection until you have a chance to scan it for indicators of compromise.
A true story
When I was in grad school the computer systems in our department were hacked. It turned out it was hacked because a malicious attacker got a hold of the username/password for one of our users, connected in, and then managed privilege escalation from there. Being young and naive I made a comment to my advisor along the lines of "Who can be stupid enough to share their username and password???". My advisor quickly answered with: "Actually, that was me." (which obviously left me feeling like the idiot, and taught me a valuable lesson about not jumping to conclusions or running my mouth). He then explained:
He had been visiting a different institution and connected to their systems. He did not realize that their server was compromised (they didn't know it yet either). He then ssh'd into his own account in our system, and in doing so the compromised system had no problems at all reading his username and password and sending it back to the attacker (the ssh client on their machine had been replaced with a malicious one). They were then able to use that to get into our system and go to town on our servers. All that to say:
The biggest risk of connecting to a compromised machine is that you must assume that absolutely everything you do will be recorded and sent off to the attackers. Do not connect to any other systems from the compromised machine. Do not connect to your email from the compromised machine. Do not connect to any websites at all from the compromised machine, unless it is the sort of thing that you wouldn't mind posting publicly on the internet along with all of your access credentials. Granted, this probably goes without saying, but I've found that sometimes leaving the obvious things unsaid comes back to bite you later.
Your actual question
Of course this isn't exactly what you were asking about. Presuming you don't do anything important on the compromised machine, there is certainly still some risk involved in connecting to it. I would expect the risk to be low as it (seems) unlikely that the compromised machine will be able to directly infect your machine. It's certainly impossible to rule out a zero-day vulnerability that may allow the remote machine to take over the client, but it is probably a lot easier to spread over network connections then hacking backwards through the RDP protocol, so I doubt there are really many viruses/rootkits/etc. that actually do that. There are other resources shared between client and server that you will have to watch out for. Still, given how easy it is to setup a virtual machine, I would consider it a reasonable precaution to connect through one:
- Spin up a virtual machine
- Use the virtual machine to connect to the compromised RDP server
- Trash the virtual machine afterward.
Your mileage will vary. We all have different level of risks that we are willing to accept, and different levels of "inconvenience" we are willing to undergo to avoid those risks. I don't keep up on the RDP scene (I'm a linux guy), but in a quick search I found plenty of RDP security vulnerabilities but none that appeared to allow the remote system to gain control over the client. An additional layer of security might not hurt, but remember to never trust anything from the compromised machine or do anything of any value at all while there.