I'd never run a laptop without the battery connected. I've repaired one laptop for a neighbour who regularly ran it without the battery. She doesn't, any more.
Depending on the design of the power system in the computer, it may rely on the battery to stabilise the voltage on the power bus. If it's a 12 volt battery, the charger may deliver anything up to 18 volts off-load. Without the battery, components expecting 12 volts will get 18 volts and the magic smoke starts to leak out...
That's unlikely to affect the CPU or the memory, because they run from a stabilised supply far lower than the battery voltage, but in my neighbour's case it killed the hard drive which wanted 12 volts and didn't like the amount it got.
Simply put: overvoltage hits devices with the square of the overvoltage percentage. 20 percent too many volts, with no regulation, means 20 percent too much current, which means 44% too much power. Heat and smoke escape follow.