Not quite exactly, but there are several things that can automate things the same way.
The two main mods for early-game automation available in Ultimate are BuildCraft and RedPower.
If you want to use Buildcraft, you'll need to craft some Transport Pipes. Place a Wooden Pipe adjacent to a chest (or any other block with an inventory, i.e. furnaces, other machines), and some Stone or Cobblestone pipes connecting the wood pipe to wherever you want it to go. Place a Redstone Engine adjacent to the wood pipe (make sure it faces the pipe), and give it a constant redstone signal. It will pull one item from the chest at a time, and it will gradually heat up and pull items faster. Don't worry about redstone engines exploding.
Note that there are more advanced items and pipes in BC, such as Autarchic Gates that can run wooden pipes more compactly, without engines, Gold Pipes that make items go faster, Diamond Pipes that sort things, etc. These are more expensive, though, and would be difficult to explain in a short paragraph.
Alternatively, there's RedPower. What you'll want to do is craft up a Transposer, some Pneumatic Tubes, and a redstone clock of some sort (RP has its own single-block redstone clock, called a Timer- I'd recommend it), like you'd use with a Dropper. Place the Transposer adjacent to the chest, making sure that the side with the large hole is facing the chest, and the side with the small hole is facing away. You can use a Screwdriver to rotate it, if it's facing the wrong way. Connect the tubes from the back of the Transposer to the appropriate destination, and connect the Transposer to the Timer (or vanilla redstone clock).
On each pulse, the transposer will pull one item from the chest and push it into the tube behind it; from there, the item will move through the tubes toward the nearest inventory. So if the tube line is connected to several different chests, items will go first into the chest nearest to the transposer, and when it fills up, the second one, etc.
Tubes also have the advantage over pipes that they will always send items where they are able to go, and will never drop items on the ground. BC Pipes, on the other hand, will usually send items in random directions at intersections, and tend to drop them on the ground if they won't fit.
Finally, note that the hopper you see in NEI in Ultimate isn't the one Vanilla added in 1.5. Buildcraft's hopper has only four slots, and will only dump items into inventories below it. It cannot pick up items, pull items from inventories, or insert items into the sides of machines.
Edit:
No, there isn't. There are, however, some packs available for MC 1.5. Most notably, there's Direwolf20's pack, as well as some no-longer-maintained betas (152wgt and 152ngt) and the two new ones,
Unleashed and Unhinged. I'd recommend Unleashed, as all the mods in Unhinged are set to hard mode- and GregTech nerfs a whole lot of vanilla mechanics.