See if you can find one amongst your friends and try it first. All Zoom Lens are compromises. A teleconverter is also a compromise. Adding a compromise to a compromise increases the odds it will not do what you need. The best advice I can give is, If you are shooting Canon, stay with canon optics. There are some good lenses out there made by other makers but, If you stay with Canon you will always get at least good if not first rate glass. Avoid using El Craptar lenses.
From a technical standpoint your problem is this, As the lens gets longer, The different colors do not focus on the same plane. The coatings on the lens are to correct for the different wavelengths of the light that passes through it so that they will focus on the same plane. Any aberration will be multiplied by the tele-converter. In short, The longer the lens you use it with, the less likely you will be happy with the results. The hard part of making a bright long lens is two fold. First you need a big piece of high quality glass with no flaws and then you need the coatings to deposit on a big surface in a consistent manner. There is a reason fast tele photo lens are expensive.
That said, Tamron used to make a 300mm 2.8f fixed length lens that was sharp enough you could get away with using a tele convertor with and still get OK brightness and sharpness. I don't know if they still do. If you don't need it often you might look at finding a photo store that rents lenses. We had one in Ann Arbor. I used to rent that Tamron every so often. Nice glass.