query: can frozen meat be cooked without thawing?
Not really. You'll wind up with a nuked, dry exterior and/or a raw interior.
Though if the loin isn't too thick and you have a large stockpot, large ziplock freezer bags or a vacuum sealer, and a good thermometer, you can cook it sous vide from frozen with no ill effects, then quickly sear it afterward.
Otherwise, thawing under running water or carefully in the microwave (gasp) are the quickest ways to get it thawed and ready for roasting.
I know the original query is a year old, but I thought I'd post this information in case anybody searches for this topic. A study was done and published in the journal of Meat Science, Volume 65, Issue 3, November 2003, Pages 993–997.
"Effects of cooking beef muscles from frozen or thawed states on cooking traits and palatability "
The study reports that "[color, toughness] juiciness, flavor, connective tissue amount, and overall tenderness did not differ between steaks cooked from frozen and thawed states. However, thawed steaks cooked faster and had lower cooking losses than frozen steaks."
I had to look up what defined cooking losses and found:
"The total loss that occurs during the cooking of meat includes the losses known as drippings and the volatile losses. The greater part of the volatile loss is from evaporation of water. It may include volatile substances from the decomposition of fat and volatile aromatic substances. The drippings include fat, water, salts, and both nitrogenous and non-nitrogenous extractives.
The journal article is here: