Bear with me if this gets pretty involved. The short answer is no, based on the date of November 1814. The only actual serious land combat after mid-September 1814 was in the South, principally the New Orleans Campaign. If your ancestor saw action, it would have been earlier than this, and very likely not with the 81st Penn. Battalion.

You need to understand how the militia system and drafts from it worked in this period. Each state and territory had its own militia laws concerning details of militia liability, organization, uniforms, etc.; and the militia was under the command of the Governor. Generally, all able bodied males from age 16 up to 60 (with certain professions, veterans of the Revolution, and officials exempted) were liable to militia duty in a standing organization of companies, regiments, and brigades based on local districts, counties, and major cities. These units could be called out en masse to defend against actual or imminent invasion, for example during the attacks on Washington and Baltimore in 1814. But this was only practical for a very short time. Any distant or lengthy campaigning required regular soldiers or temporary militia units "detached" from the standing organization and consisting usually of drafted individuals. Inevitably, young, single men who had not already served were called up first by lot. Some men volunteered as individuals for such duty; and, very occasionally, a whole company would volunteer to go as a unit. The detached militia were almost always placed in federal service, as a result of a call from the President to a governor for a certain number of men. But federal authorities had no other role or control until said governor ordered the detachment made and handed the resulting unit or units over for active duty, already organized into a companies, battalions, regiments, etc.

I went into all that so that you may better understand my next statement. Because of the high number you cited, it is fairly sure that the 81st Battalion was part of Pennsylvania's standing militia organization, and the drafts from it would have been placed into a detached unit either known simply by the name of its commanding officer or by a much lower number (which, confusingly, probably duplicated that of one of the standing (or sedentary) units. Over 400,000 American militia served in the War of 1812, but never at one time. The period of actual service could run from a mere matter of days up to several months, but even a populous state like Pennsylvania would hardly have had more than 80 battalions in service at any one time.

Most "active" militia service consisted of garrison duty and routine patrols, but Pennsylvania militia did see combat in the field, notably during the summer of 1814, when Peter B. Porter's brigade of New York and Pennsylvania militia and volunteers formed part of General Jacob Brown's army on the Niagara frontier.

You may well already be familiar with Pennsylvania records. The state archives have been very active, reaching well back into the 1800's. They have placed a vast amount of material concerning the American Revolution and the Civil War on the Internet, but much of it consists of scanned or photographed records in printed or typescript format which is not machine readable; therefore, one cannot locate particular individuals or facts through web browsers, such as Google. You have to go to the Penn. Archives website, figure out their organization of material, and plow through it using their own indices or other finding aids. The situation is most likely the same for their War of 1812 material.