No, hibernating shuts the power down entirely, and standby will stop your downloads too. Keeping your laptop on a hard, flat surface can help keep it cool.
I'm afraid putting your system to sleep or hibernating it will pause the download. It is quite normal for a laptop to get warm, but make sure it is on a hard flat surface and the vents are not covered. If your vents are on the bottom (why manufacturers do this i'll never know) *Yahoo error 999 prevents me from telling you what to do*. Email me if you want to know,
If the laptop is getting hot, you may want to get compressed air and blow out the vent holes to remove any dust.......While in use, make sure there is adequate ventilation around the machine and avoid placing on soft surfaces as these will insulate and maintain heat rather than dissipating it.
It is normal for the laptop to get warm, but not hot to the touch.
Stand-by and hibernate will close any network connection thus stopping any further downloading.