First of all, Its not necessary to run gather schema statistics every evening. Either once in a week or month would suffice the need. Please look at the following note:
How Often Should Gather Schema Statistics Program be Run? [ID 168136.1]
With respect to your question:
Sys and system users are not included in the "ALL" specified parameters in gather schema statistic program. It includes the list of product related users. But it is recommended you collect statistics for sys and system users and you can automate and achieve this by creating a job and schedule it at DB level. Please follow the following note which will assist you:
EBPERF FAQ - Collecting Statistics in Oracle EBS 11i and R12 [ID 368252.1]
I just have a question about the 'Gather Schema Statistics' concurrent request.
We run this every evening on ALL schemas, however our SYS and SYSTEM schemas aren't registered in the application so therefore stats aren't gathered for these.
Should SYS and SYSTEM be registered and stats gathered for these 2 schemas every night?
Please see the following links.