Yes. The load won't be a problem at all, assuming the transmission shifts smoothly and hasn't been abused at this point.

However, if you go to the Integra FAQ, you will notice that the GSR and Integra Type R (aka ITR) transmissions have tighter gear ratios with a numerically higher final drive. The higher final drive ratio will exploit the strong mid-range and top end power of the motor and produce faster acceleration times.

If you go ahead with an LS-VTEC motor, you will get the most benefit out of a GSR or ITR transmission. And yes, even if you decide to turbocharge your LS-VTEC, the GSR / ITR trans is still a worthwhile upgrade.