I purchased a Saniflo toilet for the basement, can I add a shower drain to it without using a sewer trap under the shower?

Toilets don't need separate traps because they self trap. Your shower will need one, either in the slab or under an elevated riser.

Like Ma0641 said, you need to install a PTRAP under the shower as well as at the sink if installing that. These fixtures will also require individual vents... the saniflo vent can connect into these vents and then you can send that combined vent off as one vent to connect into an upstairs vent (or vent in the basement if present).

Look at the manual included with the unit, or go to Installation of pumps, grinders, and toilets for the home | SFA and download the installation istructions as they have some great daiagrams showing how to plumb/vent all this!

Mark