Are there known performance issues when setting up SQL replication using a remote distributor?
Yes, because there is an extra network hop when using a remote Distributor. The network can be a potential bottleneck and can affect Publication database log size. Microsoft recommends a fast network of 100 Mbps or faster.
Would adding RAM or processor power avoid performance impact?
Yes, Replication agents can take advantage of processing power and adding RAM to the Distributor will improve performance by allowing it to cache more.
How much more (RAM/Processor power) would you recommend?
This really depends on your workload. I would recommend setting up a test/development environment which mimics your production environment as closely as possible and develop a performance baseline to determine resource consumption under a typical workload. Some other things to look at would be latency, throughput, concurrency, and duration of synchronization.
Here are some resources that cover replication best practices and improving performance:
Best Practices for Replication Administration
Enhance General Replication Performance
I hope this helps.