My opinion is that what you ar saying is about right. You will see more stars, but most DSO's will still be somewhat out of reach.
Oddly in optics the 7x35's will produce a brighter final image then the 12x50's. The 12x50 image will be bigger by proportionally more then the increase of light collected. Not by much but slightly. There is also the possibility that the 12x50's are stopped down internally to reduce aberrations, unfortunately not uncommon. So a 50mm lens at the front to sell the things and stopped down to say 46mm internally to deliver an acceptable image. There are other options to reduce the effective diameter like under sized prisms.
M33 I would have said would be visible, although depends on the general light level/pollution where you live.
They will not show most/all the messier list objects. Quite a number of those are both small and dim. M57 and M1 being 2 difficult ones. I may have seen M1 in a 6" scope (still argueing over that) and not seen M57 visually yet - and it is fairly easy to point to). So 12x50's are not going to do them and I suggest a number of others.
Easy targets at present would be M42, M45 then many of the open clusters - M36, M37, M38, M44, C14, C41 (Hyades with Aldebaran) is easy, there should be a good number of OC's. Not sure any planetary nebula will be easy/possible. They are generally small and dim. Globular clusters - less of those - maybe M3, M13 in Hercules is appearing around 22:00 but still low. M92 in Hercules is a little higher but still low.
There are lots of open clusters, all with assorted designations and few will "stand out". There are 6 inside Auriga only the Messiers (36, 37, 38) sort of jump out at you, and I think one of those is pretty loose. The other 3 are easily missed. Look at it this way Messier didn't log them.
Load up Stellarium, set you Lat+Long and set the time for when you are likely to be out and see what Stellarium shows are visible.
As said lots of open clusters but basically all in the Milky Way so can be difficult to say "Yes, seen it". Equally that is where open clusters form - in the Milky Way.
Have said other times: It is time to engage brain and work out a set of reasonable targets.
Make a short list of say 4 or 5 and where they are. Then go and find them. Keep a record. Old fashioned book and pencil/pen works amazingly well for it.
Search out "The astronomy league", they have an assorted set of observing programs. Dig out their Binoculoar Program, if they have an easy peasey beginners one start there. The easier the better. I still use the easy ones 20 years in and with 8 scopes and 4 goto mounts. But easy is good.
Add in a location, helps to know where you are.