Is there a way to output a Redstone signal from a custom block with a procedure?

you could try by making 2 blocks

You can do it by adding redstone power on the block, make the block a tile entity, make a procedure called WhenCustomBlockTrigerred

Set NBT integer tag "RedstonePower" of block at (x) (y) (z) to [15]
Wait [100] ticks on server-side
do
  Set NBT integer tag "RedstonePower" of block at (x) (y) (z) to [0]

Then add a procedure called GetCustomBlockRedstone

return integer (Get NBT integer tag "RedstonePower" of block at (x) (y) (z))

call the first procedure when the block is trigerred, call the second one by changing the "Fixed" field in Advanced Properties