I would say no - and for several reasons.
First, most of the "evidence" touted - especially on the show you mentioned - has to do with ancient, "primitive" man apparently having access to knowledge and/or technology that they supposedly could not have obtained on their own.
Second, the rest of the "evidence" is extremely anecdotal and circumstantial at best. We have drawings and depictions of thing that "kinda, sorta" or "could possibly" resemble aliens, flying saucers, etc.
As for the first set of "evidence", I attribute that primarily to mankind's arrogance - of which we have in massive overabundance if we have any at all. We have a major habit of both over-esteeming our own understanding and accomplishments while virtually dismissing that of previous civilizations or even previous generations. The ancient Romans made stronger, longer-lasting concrete than we make today. Many of the roads and bridges they built are still being driven on today. Much of their aqueduct system could still be used for plumbing and irrigation purposes with just a modicum of maintenance. The ancient Greeks had a "programmable" device that can only be described as a primitive computer that could be used to calculate both latitude and longitude at sea - something "modern" man wasn't able to accomplish until the late 19th Century.
To further exemplify the inconsequential nature of that "evidence", you can juxtapose that hypothesis with the second set of "evidence" given. If extra-terrestrials did, in fact, come to Earth and share advanced knowledge and technology with ancient civilizations then the recorded evidence would not be anecdotal and circumstantial; the evidence would be obvious. We wouldn't have small, random smatterings of things that "kinda, sorta" look like aliens and "could possibly" represent flying saucers; we would have detailed depictions and accounts of these encounters - perhaps even names for the aliens and examples of their language - and of the knowledge and technology being passed on by them.
The most obvious, if not most common, retort to this argument would be to ask "What if the aliens didn't want to just come out and reveal themselves to ancient man, and ancient man only caught glimpses of their presence?"
To this, I would proffer that any intelligent being capable of travelling billions of light-years across the galaxy in order to study a primitive planet would - assuming they didn't want to reveal themselves to the indigenous population - be perfectly capable of actually not revealing themselves to the indigenous population. They wouldn't be "accidentally" letting us catch glimpses of them and they certainly wouldn't be crash landing in the middle of the desert in Southeastern New Mexico.
If they had been here, interacting with mankind, then we would know it. We wouldn't suspect it; we would know it.
If they have been here but didn't want us to know about it then we wouldn't have a clue.
