Yep, however I would categorize the GCC countries in groups. They all do not have same agenda. They have differences in their agendas and foreign policies.
Group1: Oman, Qatar:
These countries always try for mediation and genuinely wanted no military action on Iran. Israel is very anti-Qatar, it even attacked Qatar not so long ago. Israel has always accused Qatar for funding Hamas. Oman maybe even at side of Iran as far as strait is concerned.
Group2: KSA:
Its defence strategic alliance is always with United States. However, slowly it has started to diverse with Pakistan and perhaps will try to get some Chinese hardware & partnerships without getting eyebrows raised at Washington.
Group3: Kuwait, UAE, Bahrain.
These countries are overwhelmingly linked with US based strategic architecture, two are abraham accord members. Bahrain had a US 5th fleet Naval HQs. Kuwait was used for HIMARs attacks on Iran, Kuwaiti airspace was constantly used (F-15s instance proved that). Also this Group 3 is more closely aligned with Israel & India.
So, I think Group 1 wouldn't be too much concerned and might be actually happy for the way things are ended. KSA wouldn't be extremely bothered too. Group3 might be very concerned for new status quo and may feel insecure the way things are heading.