No. For most vehicles you will use an Insta-dapt fitting that is included with the transmission cooler and that connects directly to the OEM transmission cooler. Then the rubber hose going to the aftermarket transmission cooler is clamped to the fitting, and the hose coming from it is slipped over the original line and clamped. Or, the Insta-dapt is installed in-line between an OEM hose and the transmission cooler hose.
In addition, some vehicles will require that you cut and flare the OEM steel or aluminum transmission return line and then clamp the transmission cooler hoses directly to the two ends of the cut line. Note: Many installers prefer this type of installation because they already have the cutting and flaring tools and no extra fittings are needed.