Yes and no.
No because that side of your hand is where your grip strength comes from, so if that is compromised than you will have some trouble holding the weight.
Yes, because its a jammed finger. You can find a way to work around that and still get some good training in. Buddy tape your ring finger to your pinky and you should be fine.
If not, you still should be able to train.
If you wait till it heals and the pain and swelling go away, you will be waiting months. Fingers do not heal fast and swelling usually never really goes away (it does, but the scar tissue is there forever).
My advice, train with it. Its just a finger. You will have worse injuries to deal with than that over time
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