SYSAUX used space close to 100%
That depends-- are your data files set to autoextend?  If they are, they'll just grow themselves up to whatever limit you may have set (or to the size of the available disk).  If not, whenever the database tries to allocate the next extent in the tablespace, the operation will fail and whatever is trying to write data to a table in the SYSAUX tablespace will fail.  There are many products that you might install in SYSAUX and any one of them might be the unlucky one that needs to allocate the next extent so you can't really predict what impact that would have.  I'd guess that you'd stop being able to write audit information since the audit trail is commonly in SYSAUX and commonly the most prevalent user of space among products that are commonly installed in SYSAUX.

You can check whether your data files are set to autoextend by looking at the autoextensible attribute in dba_data_files.

select file_name, autoextensible
  from dba_data_files
 where tablespace_name = 'SYSAUX';