I've got several laptops, with quite a few over 5 years old. If your workplace has provided laptops that are expected to be used closed, then clearly designs have changed a little. News on batteries, not going from any specific laptop-related 'went bang' but battery-related 'caught fire' or 'went bang' items, such as the (big) battery on Boeing's plane.
My mobiles, tablet and laptops get warm when recharging and discharging. It's a chemical reaction and while I did the theory some 40 years ago (about lead-acid batteries) and the technology has moved on to Lithium, there are similar principles concerning energy causing heat in the components. All I'm saying is I wouldn't run any of my laptops closed.
YMMV, I just wouldn't risk it...
OP - if you're running your laptop without the battery, but closed, then yes, that should be fine. No doubt many will have seen (on phones or in instruction booklets for laptops) warnings about turning off the charger when battery fully charged.
Partly it is because of saving energy (and your utility bill) but also because the charging introduces heat and to excess could damage some (perhaps older!) batteries. Should be fine with no battery in.