That's super rude, Dave, and not helpful at all, since it doesn't even bother to address OP's question. Obviously OP knows SOMETHING about framerates, or he wouldn't have bothered to use drop-frame terminology in the first place, let alone asking the question at all. Perhaps he misremembered 119.88 as 119.98. Rather than nitpicking him on a totally irrelevant detail and ignoring the substance, you could address his (actually very intelligent) question. You don't just say "It ought to." Do you know? Do you have facts? Or are you just saying what should happen in your opinion? How does that possibly help Jon?
Here, watch this:
The answer, Jon, is that yes, Premiere can do what you want it to do in this case: drop a 119.88 clip on a 29.97 timeline, and Premiere defaults to a "Frame Sampling" interpolation method, which grabs every fourth frame and displays it to you when you hit play (or export). You can change it to a Frame Blending interpolation which will overlay multiple frames to create a semblance of motion blur. By the way, I noticed that you wrote 119.98 rather than .88; you may want to double check that, so you can use the correct math to slow your footage down, since 119.88 would normally be the correct number.
When you slow the clip down, whether through the Speed contextual menu, or via the Time Remapping keyframes in the Effects panel, Premiere will show as many frames as possible within the native timebase of the project. So if you slow the clip down to 25% speed, you will have one frame of footage for every frame shown on the project timecode counter. Go to 50% speed, and Premiere will show every other frame if you are Frame Sampling, or blurring every two frames together if you are Frame Blending. Go to some other rate, and Premiere will do some combination of the above.
I just tested this myself to make sure, by dropping a 59.94 clip onto a 23.976 timeline, slowing it down to different rates, and then watching the motion as I went frame by frame. This knowledge will be relevant to the way I work with offspeed footage in the future, and I'm glad you asked so I could take a moment to test this. Now we both know we can do it either way. Great question!
Will just add that I just edited a Premiere CC project using 60p clips in a 30p sequence (59.94 and 29.97 to be technically correct) and when applying 50% speed, slow-motion was silky-smooth, beautiful!