Well, I think it depends on a couple factors, and season 4 isn't a great resource for answering either question:
- (An old standard) - How does branching work?
- What kind of technology do the Kromaggs have?
- (Secret third question) - what is the definition of "conquer?"
Let's start with technology. You're right in the sense that technology and surprise would make an invasion pretty easy. The Kromaggs could send in human slaves (or even their own scouts, if properly disguised) to scout the world - find the military powers, and strike. They could slide wherever they want and wipe out military bases with very little damage. Imagine a Pearl Harbor-like attack from a Japan we didn't even know existed on a global scale. The US, China, Europe, Russia, the Middle East, India/Pakistan wiped out simultaneously. It'd take a coordinated attack, but I'm not even sure it'd take that many troops.
So invasion is easy.
Now let's talk about what "conquer" means. Does conquering mean that they held the area indefinitely? Or would it count as conquering if they simply took control for a long-enough time to take what they wanted (slaves/resources) and get out? When they say they've conquered 150 worlds, are they still maintaining a presence in all 150?
And if they maintain an indefinite presence, does that necessarily mean that all soldiers on the conquered Earths are Kromaggs? Look at the world in the USA show Colony. Aliens (allegedly) invaded and conquered the Earth. Then they set up a provisional government led by human traitors. Not a single alien boot on the ground, and the Earth is still conquered. If the Kromaggs used mind control or simply the threat of additional force, would that be enough? Would Kromagg weapons in human traitor hands be enough to hold the worlds?
And if it was, could a skeleton crew of Kromaggs (skeleton being as few as possible - a million? less?) hold the Earth with advanced-enough technology? In Colony, there are drones all over the place. Could that work to keep an Earth "conquered?"
Now let's talk about one of my favorite topics - branching. As far as I'm aware, branching happens all the time with each decision. Whether it's only big decisions (George Washington is shot or not) or minor decisions too (do I get a chicken or steak in my burrito) is up for debate, but either way, it's decision-based.
And the human/Kromagg decision was a looooong time ago. Enough time for millions of human-led worlds to be created. Presumably, that would also mean that there would be enough branching from Kromagg-led worlds to create millions of Kromagg-led worlds. I always assumed that the Kromagg dynasty was made up of thousands of Kromagg worlds that united. If that's the case, there's a nearly-unlimited source of additional troops to hold (way more than) 150 worlds.
"Kromagg Prime" implies that it's the main homeworld of the Kromaggs, but our sliders call our world "Earth Prime" arbitrarily. To Logan, her Earth would be "Earth Prime" and ours would be "that weird Earth where the trains suck." So I always thought it was just that type of naming.
(Please note that there's a chance that almost all my arguments are invalidated by season 4, which I haven't seen in a really long time).