If the VA benefits will pay for all or most of the cost of the type, by all means, go for it. If getting the type is on your dime, then it's a harder question. Advantages of doing the type rating course and getting both at once:
- better preparation for the ATP ride. The "ATP-in-a-weekend" courses will have you feeling BARELY comfortable in the Duchess (or whatever they use) by the time you take the ride. It'll probably work for you, but you'll feel MUCH more comfortable with the sim taking a type rating course.
- the training is a good preparation for the way the civillian flying world does business and does training at the airline level.
- The 737 type is not going away soon as a gotta-have-it for a job with SWA, and it's about 99% required for an interview. If SWA is an option you're considering, having the type makes you competitive; lacking it means forget about it.
Advantages to NOT getting the type:
- save a fair bit of cash (if you're paying for it)
- some possible "holding out for SWA" stigma. Some places won't care, others will accept a thoughful explanation for why you got it, others will nod & smile and figure that you're really hoping for SWA regardless of what you say, and unless they're willing to be a "temporary job" until #1 makes an offer, they'll slide your app to the side.
- For an A-10 driver, I strongly doubt having a 737 type will prove very much to the likes of Jet Blue or AirTran or FedEx in terms of "he can handle -121 training." If you'd been flying Canyon tours in a caravan, or a turbine crop duster for your turbine PIC time, I'd say it would add some "he's trainable in this environment" credibility... but you aren't hurting for credibility in the realm of high-performance and IFR flight.
Again, if the type training would be paid for by somebody else, I'd say by all means go ahead & get it, because the schools (HPA and K&S particularly) have very good training programs. If you're footting the entire bill, I'd be much less certain... could well be worth saving the several thou difference between an ATP course and a type course.
FWIW, I did my ATP ride in the 737 sim as my 737 type ride... but I also knew I wanted to go to SWA as my first choice. YMMV. Good luck!