Yes or no. Forget that frames even have a size. Measure top tube lengths and compare. Given the wide variation in how frames are sized, you may find that a 60cm from one brand will be too big and a 62cm from another is too small. Top tube length is a universal measurement that can actually be compared across brands (make sure to always use the 'virtual' measurement if it is a sloping top tube). If you know the top tube length on your current bike and like it, all you need to do is find another frame within +/-10mm and have at it.

You may also want to consider head tube length depending on how aggressive or relaxed you want the fit to be. Since you own a frame already you have a decent baseline from which to compare other frames.