I'm trying to simulate what you have there to understand what you're getting at.
I understand with say, no resistance whatsoever, like you might use with a plate choke for a common-grid amplifier, you need some resistance to damp the oscillation. Here's an example with a BFU590G I did simulating a common base with an inductor to the supply. Clearly there is oscillation, as one has the oscillation of the collector-base capacitance and the inductor. The transient analysis shows the rise of the oscillation.
But it doesn't really make sense to do this, I think. A common-base usually has a resistor at the collector, and then you don't get this sort of oscillation. You could use a combination of the two, which is perhaps what you're proposing?
But if I add inductance to the base lead, we can clearly see the oscillation starting, which is the prime issue with trying to do common-base amplifiers. I chose the value based on the information in the SPICE model file.
You can see the resonance peak after the base inductance is added. This is the primary problem with common base I think, that the base grounding is imperfect. An effective way to get rid of this is to add a base stopper resistor:
However, this has a noise and gain penalty. Adding an emitter resistor lowers the gain, adds noise, and raises the resonance frequency.
So you can decide what kind of situation you think is best. I included a zip file of the Qucs-S simulation if you want to play with it, including the BFU950 spice model.