If you really want to go through this effort (rather than just capping off the lines), then you should just install the lines into the walls (if they aren't already).
![plumbing in walls](https://i.stack.imgur.com/86dCW.png)
Normally you'd just cap the lines off until you're ready to hook everything up (as seen in my picture above), but there's nothing stopping you from putting valves on instead of caps, which is a great idea anyway (it makes it easier to hook up, service later, etc).
With the pipes in the walls, you can freely work on the floor and install cabinets without worrying about them (and as you can see in this photo, it was before I had flooring or cabinets in).
Here's the same connections (with valves) after installing cabinets and the new sink:
![enter image description here](https://i.stack.imgur.com/EcY0I.jpg)
Nothing stops you from using valves instead of caps, though it does require cutting a bigger hole in the cabinet to install. Depending on your cabinet style you may or may not like this -- in my case these are pretty cheap cabinets installed in a laundry room in the basement, I wasn't too worried.
Just be sure you don't accidentally knock the vales open while you're working, or you'll ruin the floor that you're not even finished installing yet!
When you purchase a P-trap from the hardware store, you'll end up with these pieces (or something similar).
![P-Trap pieces](https://i.stack.imgur.com/SPqSt.jpg)
You'll also want to pick up a 1-1/2 in. PVC 90° slip-joint elbow while you're there.
![1-1/2 in. PVC 90° slip-joint elbow](https://i.stack.imgur.com/bRsEcm.jpg)
You'll then want to connect the pieces something like this...
![Connect these pieces](https://i.stack.imgur.com/fudVw.png)
You'll then have to twist the pieces around, until you can get them to fit together. You'll end up with something similar to this.
![twisted p-trap](https://i.stack.imgur.com/adQQ8m.jpg)
![twisted p-trap](https://i.stack.imgur.com/z0rGp.jpg)
Though I'm not sure this is code compliant anymore.
In the 2003 version of International Residential Code (IRC), there was this section.
International Residential Code 2003
Chapter 31 Vents
Section P3105 Fixture Vents
P3105.3 Vertical leg for waste fixture drains. A vertical leg (see Figure P3105.3) is permitted within a fixture drain of a waste fixture in accordance with the following criteria:
- Minimum trap diameter shall be in accordance with Table P3201.7.
- The diameter of Section A shall be equal to the diameter of the trap.
- The length of Section A shall not be less than 8 inches (203 mm) and in accordance with Table P3105.1.
- The diameter of Section B shall be one pipe size larger than the diameter of Section A.
- The length of Section B shall not be more than 36 inches (914 mm).
- The diameter of Section C shall be one pipe size larger than the diameter of Section B.
- The total length of Section A and Section C shall not exceed the distance allowed in Table P3105.1.
- Bends shall be the diameter of the largest connected section.
![FIGURE P3105.3 VERTICAL LEG FIXTURE DRAIN SCHEMATIC](https://i.stack.imgur.com/ZyMxc.png)
However, in the 2006 version, this section is gone.
Best Answer
Horizontal - no.
No drain line is EVER horizontal. Unless someone was an idiot and should not have been plumbing....
Perfectly acceptable to run at an appropriate slope, however. 1/4" per foot (or 2%) is the standard minimum slope for small drain lines like this.
How will you handle the venting? That is a complex process for island sinks, and if it was a peninsula before probably not arranged for. You mention having a "wall behind" - can your vent run through that (is your island not an island in the usual sense?)
There are ways far less drastic than a jackhammer to get into concrete and rearrange plumbing.