Disabling Resource Governor in SQL Server
I change Resource Governor settings quite often without restarting SQL Server. I am not aware of any need to restart SQL Server after changing Resource Governor settings except possibly for a classifier function change. A few things that might be helpful to know:


Once a session is assigned to a Resource Governor workload group it stays there, even if the classifier function changes.
I have never seen query plan compilation account for Resource Governor settings.
Some aspects of query execution are decided at the start of query execution, such as MAXDOP and query memory. Note that there are some exceptions where that isn't always true such as certain types of index creation or queries that execute in batch mode.


A precise answer that fully answers when the changes are applied to queries (whether or not it is "instantaneous") is likely outside the scope of an answer here. I suggest figuring out what you care about and doing testing as needed to convince yourself that what SQL Server is doing is okay with your workload. For example, consider the MAXDOP limit available through Resource Governor workload group configuration. For nearly all queries MAXDOP is decided at query execution time, so I wouldn't expect disabling Resource Governor to change the MAXDOP of a currently executing query. However, the next query that starts for the session will no longer be limited in MAXDOP. However, what happens if there's a Scalar UDF executing many times during a query with a parallel plan? I'd expect MAXDOP to possibly change for that query, but I've never tested that and don't care to test it. If I had to guess, I suspect that all of the following will be updated "instantaneously":


MIN_CPU_PERCENT 
MAX_CPU_PERCENT
CAP_CPU_PERCENT
MIN_IOPS_PER_VOLUME
MAX_IOPS_PER_VOLUME
IMPORTANCE
REQUEST_MAX_CPU_TIME_SEC
GROUP_MAX_REQUESTS


and all of these to update only after the next query starts executing:


MIN_MEMORY_PERCENT
MAX_MEMORY_PERCENT
AFFINITY
REQUEST_MAX_MEMORY_GRANT_PERCENT
REQUEST_MEMORY_GRANT_TIMEOUT_SEC
MAX_DOP