Short answer: Yes.
The Slider's battery is decent, however the phone itself behaves like an overclocked Optimus V... the processor is set at 800Mhz, rarely ever performs below 800Mhz. To give you an idea how grueling that is, modders have found that going any more than 850Mhz will make the processor overheat and crash the phone.
Can you fix it? Yes... Root and NoFrills should allow you to make the governor a little less power-intensive (set to Ondemand instead of Performance), and JuiceDefender helps with mobile data consumption/draining a bit. Overall though, a more powerful battery would be nice.
I wouldn't recommend heavy usage with low signal while charging... dunno if I'll make my poor Slider freak out by doing that now.