Is movement in my bottom bracket an issue which requires attention immediately?
I'd suggest you try tightening the Non Drive Side cup and see if there are any improvements. 

You don't even need to remove the crank for this.  The right tool will just slip on, or you can get away with a big spanner and some plumber's sliding jaw grips.

If this helps the problem even a little, a proper clean and regrease will help a lot more.



The risk in not doing this is that there will be damage done to the cones in your BB, and if metal flakes off the inside surfaces where the bearings run, then its toast and you will need a replacement.  A cartridge bearing is relatively cheap these days, and is well worth doing even on a beater bike.