Oh, so there is a 60hz mode on the PAL games already? I wasn't sure if it was something that was placed on the cartridges to start with or not back in the day. That is good to know then.
The short answer is it depends.
Especially for the first several years of the console's life, a lot of games released in PAL regions were not optimized, and run in PAL regions at about 5/6 of the speed they do in other regions. Sonic 1 is a notable example. At the same time, many of these games did not engage any form of region lockout (which is done in game software, not a hardware feature). The basic takeaway is that these games were the same ROMs in different regions. Something like Super Fantasy Zone is a game that has Japanese text on a Japanese machine and the same cartridge will have English text on an outside-of-Japan machine. It will run in (IIRC unoptimized, slower) 50 Hz mode in Europe, and 60 Hz in America despite not being released there. Japanese cartridges had different case shapes but the actual PCB underneath it will be the same for most games up until, like, partway into 1992.
Streets of Rage 2 is the first Sega-published game I know of with region lockout, and it's also I believe well-optimized for 50 Hz (i.e., not obviously slower). There are ways to use things like Game Genie codes to unlock them for other regions (because, again, all region lockout is part of the game code, not a hardware feature). Sonic 3 was the only Sonic game to have region lockout. Some games in this era had the lockout specifically because they were big enough now that they couldn't fit both the PAL code and the 60Hz code in the same ROMs any more. It would drive up costs for limited benefit. This is, however, not always true. Sometimes the games only had two modes, one for Japan and one for outside it, with the main difference for the split being not enough space for the localized text and Japanese original text.
Very late into the systems life, PAL games took advantage of the slower refresh rate to expand the vertical display of some games. Ristar in particular comes to mind as a game where this occurs. It's a subtle effect though and for me doesn't make up for the slower refresh rate (though, again, Ristar is optimized enough that it's not obviously slower for PAL players), though it would be nice if there were ways to use the recreated hardware to play the game at 60 Hz with the increased vertical resolution.
(I will not stick my neck out and say that this higher-res mode is the one that the Overdrive II demo uses to draw into what would otherwise be the overscan area, as I haven't worked with the technical documents enough to say for certain. I would assume so. It is technically available on NTSC units as well but requires more considered use of CPU cycles when actually doing anything with the system since the time between frames is shorter, which is why it was never used in any commercial game I'm aware of.)