No; most mods won't even work on a different minor version (1.12 vs 1.12.1 vs 1.12.2) since even if the code they rely on wasn't changed Mojang obfuscates the game and it changes with every update (if you look inside the Minecraft jar you'll see a bunch of files with names like "abc.class"; while Mojang does not ban mods they do not support them either and this is common practice to deter people from reverse engineering a program). Some simpler mods can get away with this if they entirely rely on Forge or another modloader to hook into the game (not making any direct references to anything in the game); either way, 1.12-1.13 is entirely out of the question due to the huge internal changes, so much that Forge only recently released a beta for 1.13 half a year after it was released and many other tools and utilities have yet to update.
All mods stick with a version they are made for. I even tried 1.13 Forge Pre-Release Mods and 1.13.2 Forge mods and they don't work, so even if it's 1.12 mods you attempt to get working for 1.12.2 it won't work. Unless the developer allows support for multiple of the 1.12 to 1.12.2 range of version then yes, otherwise no. Same case was for 1.9.4 & 1.10 versions, unless they were close enough in support they won't be able to work. Also 1.13 had a lot of reworking so less likely is it to for a simple 1.12 to 1.13 port because it's just not that easy.
1.13.2 Forge mods shouldn't take long to come across, but the big ones will as usual, I'm curious about all the small tweak ones or small content ones that come out that are new since I find their a lot of fun. Had this mindset with 1.8 all the way up to 1.12 in their early stages and found some awesome mods I still use today that have been available for those versions, but I know not everyone has my 'enthusiasm' and would rather stick with what their used to and there is nothing wrong with that at all since I do both anyways.
Also what I noticed is you can't used 1.13.2 mods in a 'mod folder' of it's own. 1.12.2 and before you can, Rift you can't, Fabric not tried or had much success with either. So that's also a 'thing' that's disappointing, unless it's just for the 1.13.2 Forge Public Beta and with later versions of Forge it might be a thing, or they just ditched it/it's not supported because Minecraft can't recognise it.
'Niche Community Content Finder' for fun and support of creators. I just swim through my 'Experimentation Pond' of content that intrigues me or really needs a bit of acknowledgement or bug fix testing/reporting. I also make modpacks/maps
Creator/Maintainer of Fabric, Rift & Tesla Mod Discussion Threads/Niche Mod Youtuber.