Interesting Question
That is a really interesting question you posed. My one word answer would be yes. The thoughts I have (Both supporting and not supporting my answer) are below.
I think JetBlue has an overall good business plan. They are fortunate to have modern and fuel efficient planes, which are critical factors in saving the company money on high fuel costs and maintenance costs. Their workers are paid reasonably (Except EMB-190 pilots), and they are fortunate not to have any pension costs. I think pensions are the largest drain on legacy carriers. This is a huge advantage for JB!
JetBlue has two MAJOR advantages over Southwest:
1) The hub and spoke system. While JB flies some point to point service (mostly to Florida), they are generally a hub and spoke airline which allows it to move passengers more efficiently, and make better utilization of their aircraft. This can be seen by their loadfactors (Soutwest 65%, JB 85%)!
2) Lower labor costs
With these advantages, there will be some things that will burden JB.
1) Their maintenance costs will increase as their fleet ages
2) Their labor costs will creep up
3) Other carriers will start to retire older aircraft, which will primarily reduce JB's advantage with fuel efficiency (MD-80's, DC-9's, and 737-200).
I think JB really has to be careful with their growth! I can't emphasize this more. JetBlue has more aircraft on order than any other U.S. airline. They need to be careful not to grow the airline beyond their ability to manage it, and they need to continue to keep costs under control as they expand!
Also, I just want to chime in that I feel none of the legacy carriers will be gone in 5-10 years. That's my opinion. All in all, I feel JB will be around in 5-10 years.