The short answer is yes, you can use the 'body' thermometer to measure other things including the surroundings - as long as the range and accuracy of the thermometer are sufficient for your needs and the materials of construction are appropriate.
Bear in mind that many temperature measuring devices require that the sensing element warm up or cool down to the temperature of the fluid or object being measured. All of that happens as a result of heat transfer. Usually the fluid or object being measured is infinitely more massive than the sensing element so the relative impact of the thermal mass is insignificant as long as you can wait long enough for the fluid/object and sensing element to reach equilibrium.
Heat transfer occurs by conduction or radiation. In conduction physical contact is required - in radiation no contact is required but the heat transfer occurs within the line of sight from one object to another. Most of the time we think of conduction and ignore radiation, especially when talking about room temperatures however the impact of radiation can be significant. There can be enough radiative heat transfer to/from the sensing element to introduce significant error. An extreme version of this effect can be seen when frost forms on the grass, trees, autos while the air temperature remains well above the freezing point. A clear night sky looks like -100 degrees F even though the air is much warmer. Radiation from the grass or whatever occurs faster than the conduction back to the object from the air so it drops below freezing.
Typcially the 'body' thermometer is design to conduct heat from the body. If it's a traditional mercury or alcohol thermometer the sensing bulb may take a little while to warm/cool in air but eventually it will get there. The sensing element in the electronic versions may not be quite as massive (relatively) and may respond quicker to air.
So, more than you wanted to know, maybe. Don't apologize for asking - it's a good question.