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If it is just a plate t-joint....then yes, welding all around covers both sides of the plate without the need of a double sided symbol.
ie.
If it was a pipe welded to a plate and the welding symbol was a double sided fillet and weld all-around, then you would have place a fillet on the inside and outside wall of the pipe where it meets the plate.(hopefully the pipe is large enough or short enough to get to the inside to perform this weld.