If I were you, I'd do a test with that thing before I risk looking meat to it. Pack it with your blue packs and leave it outside. See how long it takes them to defrost.
As for actually using them to hold meat, I'd advise against it. A combination of loose ice and those blue packs might be a safer alternative. Definitely, have the meat frozen to begin with before you pack it into the ice/pack combination.
How long is this trip for? Do you plan to hold meat for more than a few hours??
I strongly advise you to test your cooler to see how long it takes the ice to melt. Once it's melted, you are essentially holding your meat at room temperature, which, if you are outside, can easily be 80 degrees. At that point, the meat, any meat, is absolutely unsafe to eat, even if cooked.