No. Your battery degrades each time there's a cycle of charge->use. If you're lucky, you can do that a few thousand times before you lose much of your battery's capacity. If you leave it plugged in, you aren't losing cycles, so you should do that.
A cycle from say 70% to 80% doesn't wear it out much at all.
The problem with leaving it at 100% is that just sitting at full charge wears it out, it's better to just keep it within 40%-80% than to leave it fully charged.
A 40% depth discharge is going to put way more wear than leaving it at 100%. Unless you want to plug and unplug constantly most users are probably best leaving it plugged while working.
If you really want to, you can do a little bit of good by letting it drop to 40=80% during periods of non-use.
If the indicators are correct, HP's chargers keep the batteries at ~95% (varies between 95-100% all the time). So they're not keeping them fully charged or overcharged, but instead leave some breathing room.
Emphasis on "well designed". The 500€ laptops I've experienced in the past weren't and you could murder the battery like this in couple months, no matter the brand (HP, Dell).
