Short answer: NO

Access to the Gold lounge is not a benefit of any tier, not even FPC Platinum, and even the confirmed suite upgrade certs cannot be used to upgrade to a Gold room/suite nor is it possible to upgrade within the Gold category. Fairmont is very protective of the Gold floor, you can generally expect a premium of $150+ to get exactly the same room on the Gold floor.

Just to give you an example of how protective Fairmont is of the Gold floor (which they market as a "hotel within a hotel" versus the "business lounge" concept at most other hotels): I´ve been pretty lucky over the years with regards to upgrades and have received penthouse suites, multi bedroom suites etc., but not once have I been upgrade to the Gold floor. Sure you´ll find a few people on FT who will tell you they´ve been upgraded once in a blue moon, but generally it´s very unlikely to happen.

I´m not an expert regarding the Swissotel program and couldn´t find a lot of info on the Swissotel benefits site, but generally the benefits you receive at the other hotels are very limited.

For instance, FPC Premier/Platinum members can earn stay credit when staying at Swissotel/Raffles hotels, get a welcome gift and a few other benefits (see details here), but overall the cross-brand benefits are very limited and nothing to get excited about.
I´d expect that the benefits you receive at Fairmont hotels are similar to those FPC Premier7Platinum members receive at Swissotels, possibly a comp. one-category upgrade if you´re very lucky, but not much in terms of "guaranteed benefits".

One last comment regarding Gold rooms: If you book your room on the Fairmont website you may be offered a "standby upgrade" to a Gold room. Basically you´re offered to be upgraded at check-in if there´s availability for a set fee (which usually is about 50% of the price difference between the room category you book and the price of the Gold room), and of course you´re only charged if you´re upgraded, which is an excellent deal IMO.