Within reason (I mean "less than thousands", and you are no where near that) the number of databases should not affect the performance of the server. I have seen people claim to run thousands of databases on a single instance of SQL Server, and the performance of the user databases hasn't been a problem. (On the other hand, looking at those databases with SSMS is a problem, as is trying to manually manage all of them.)
Very roughly speaking the performance of the server is governed by the amount of data that is accessed in those databases and how much memory the server has. Assuming that you have enough disk space to store both databases and that you never access the "test" database, the production database performance should be unaffected. If you "sometimes" access the test database, the performance of the server could be affected at those times. You can mitigate that by testing when the server isn't busy, like in the evenings or on weekends.
All of the data in a database might not be regularly accessed. It is very common to have old records, "archives" and other sorts of stuff which remains in the production database by isn't regularly returned by queries on a day-to-day basis. In many databases, this "cold" data might be much larger than the amount of "hot" data that is regularly accessed. If the amount of hot data is very small, you might not notice any performance problems when using the "testing" database even when the production database is being used full-blast.
To make things a bit more complex, poorly designed queries and database tables might be inefficient, and return data that really should be "cold", or cause table scans.
In short, if the server can hold all of the hot data (from production and testing) in RAM, then you will probably be ok, or at least not much worse off than you are with only the production database in use.
Back to your direct question: Will adding more load be a problem?
The first thing to do would be to look at the performance of the server now. Do you have performance problems? Are those problems caused by a lack of RAM, a lack of disk I/O capacity or a lack of cpu power? There are many, many guides on the internet and StackExchange to help diagnose where your currently bottlenecks are.