While yes you can use both inputs of the amp simultaneously, a passive A/B/Y splitter opens up potential for problems such as loading (dull, weak tone) and feedback.
You can use an active splitter like the Boss LS-2 to avoid those issues. Additionally there are "blender" pedals that mix your clean and dirty signal paths going into just one amp input. The LS-2 works that way too, and there are many others (search on blender).
Also, this is 2011 and there are some fantastic bass OD pedals that don't lose any lows.
