Theoretically, yes. If it's JUST that the pins are bent, then re-bending them should solve the issue. Do be cautious not break the pins as they may be weakened from the initial bending. It is conceivable however that damage could have spread further if too much force was used...but hey, what's the harm in trying?!
Also, I've never worked on a DS Lite myself (and it's been forever since I've held one) but can't you get to the pins from the cartridge opening? If you still wanted to open her up and get a little closer to the pins, use this guide to get down to the motherboard where the cartridge unit is.
I just fixed this problem on my daughter's ds lite. The pins were not bent, but it was not reading any games. Spray a small amount of WD40 onto the game cartridge's connectors. Insert the cartridge and remove. Then use a toothpick to clean between the pins on the ds. Back to working oder!