Yes, Logic Express can control both a keyboard and the drum machine simultaneously in concert with any internal software synths, provided you have enough connectors. Your MIDISport Uno only has one MIDI Out, so in order to get both the keyboard and the drum machine to sound (and assuming that your keyboard is not otherwise connected to the computer), one of them may need to have a MIDI Thru port, in order to "daisy chain" the MIDI signals. You can search Google for some example MIDI Thru setups.
Don't forget to patch your audio cables into the computer (preferably through a small mixer), either. Remember, MIDI transfers note and controller information, not actual audio.
I'm somewhat of a Roland fan myself. My main synth controller is an XP-10. I also have a JV-880 synth module with the Vintage Synth sound expansion card that I use occasionally for atmospheric pads. My recording headphones are RH-50s, and my monitors are MA-8s. Although I don't have a true drum machine, the majority of drum samples I use are variations of classic Roland drum sounds (TR-909, some 808). The only non-Roland bits of gear I use are a M-Audio O2 MIDI controller and a Yamaha AN200 desktop synth.