Yes, you can check a cardboard box with a TV in it, as long as it is under the limits. However, United policy is that they're not liable for damage to fragile and high-value items, see here. If it is in the original styrofoam packaging, this might be sufficient, but it is still a huge risk.

And even a 40 inch TV might not be under 62 linear inches. I found specs for an average 40 inch flatscreen tv, and it gives the shipping dimensions as 46.5" x 26.2" x 5.0" = 77.7". Even the bare TV, out of the box and without the base stand, is just under 62" (37.2" x 22.1" x 2.0" = 61.3").

So to check this, United will charge a $200 oversize baggage fee. It is almost certain that shipping via a company who offers insurance for such items (DHL, UPS, Fedex, etc.) is going to be the cheaper and better option.