I am in the roofing business (in Texas) and the underlayment does do something. It is a vapor barrier to help protect the decking. It is not waterproof but it is necessary if you want your shingles to be under warranty with the manufacturer. If you omit tar paper or another type of underlayment under the shingles, it will be deemed an incorrect installation and won't be covered by their warranty. All bundles of shingles state the underlayment is required.
To the OP, I like the Malarkey shingles and I wouldn't have a problem using the Secure Start SG. It's a synthetic material (which I prefer) and it's tear resistant unlike the normal tar paper. Do make sure that you or the guys keep it pulled tight when nailing it down. I don't know your building codes out there but if you are wanting peace of mind besides the info you asked for, buy some GAF Storm Guard (or another ice/water shield) and install a strip along each eave and rake edge before installing your starter shingles and also in any valleys, around chimneys, pipe jacks, turtle vents, wind turbines, etc.... We also install it against any walls where the wall and roof touch. We apply it 6" up the wall and 6" on to the roof, then the synthetic felt, then step flashing as you are laying the shingles. It will probably cost you $300-$400 more by adding that step but it's waaaaay cheaper than having water damage (inside and outside) and having to get it repaired. If you don't add the Stormguard step but everything else is installed correctly, you should be fine. I just don't like call backs and it comes out of my profit on each job if the customer doesn't want to pay for that option and I'm ok with paying for it because it beats me having to go back later on for a leak. Good luck!