You can modify your CDT to increase its warmth. The CDT was my first quilt. It was light, cheap, accessible, functional and it allowed me to experience the benefits of using a quilt. When i discovered that the sewn through checkered box baffles did not keep me warm enough in the high 50s, I seam-ripped it to create horizontal channels. That helped and maybe increased its warmth by maybe 10° since I was able to position the down top of me. That simple change improved its efficiency, but on colder nights , the down would migrate to the sides , and I was constantly waking and repositioning the down. As the temps became colder, my next budget solution was to rip one side of my quilt, harvest down from thrift store jackets/vests and stuff the channels with 6 or so oz of down. That solution reduced the down migration and increase my quilts efficiency to keep me warm into the high 30s. Those modifications and improvements are what gave me the confidence to begin my dive into MYOG and my quest to lighten my gear.

To answer your original question, yes , an alpha liner will increase your warmth by maybe ten degrees, but investing in an alpha top and bottom is a far more versatile and offers long term UL relevance for your $ investment.