Can power actually be sent into the ionosphere for transmission?
This is a complex question to answer, especially since Tesla borders on a deity for many.  Further, I am not an expert in Tesla so it is entirely possible that I am incorrect in some of the things that I post.

In life there are certain things that should raise red flags.  For example, a Dremel tool, duct tape, or a cordless sawz-all is an indicator that something has gone horribly wrong since nobody would/should use these items except as a last resort.  There are similar indicators for when you're in a discussion about religion, politics, weight loss, etc.  In technical circles, more than any other person, mentioning Tesla should raise many red flags.  

It is not that Tesla was a crackpot, but that Tesla has been deified by so many other crackpots that it is often easier and quicker to assume that those who use his name are crackpots themselves.  

Certainly Tesla's early life was filled with successes and brilliant innovation.  But later, his life took a remarkably more disappointing turn.  It is up for much debate, but there are those who believe that he was suffering from mental illness for roughly the second half of his life (1900-1943).  It was during those years that Tesla's productivity plummeted and his promotion of vaporware and outrageous claims skyrocketed.  

Many of the ideas he put forth in the second half of his life have been latched on by the crackpot people, who assign almost magical properties to his as-yet undiscovered or undisclosed inventions.  Search on YouTube for "free energy" and many/most of the videos posted will invoke Tesla.

But his research and inventions during the first half of his life are mostly solid and demonstrate actual now-known scientific principles.  But here's the problem: Just because he showed something doesn't mean that it is practical, useful, or cost effective.  And just because people have not turned some of those inventions into modern appliances doesn't mean that there is a conspiracy to suppress them.  In many cases, they were just a scientific curiosity and doesn't actually represent something practical or economical.  

Take wireless transmission of power over long distances as an example.  It's cool.  It makes for a flamboyant demonstration.  But it is nowhere near as practical or cost effective as running wires.  The efficiency losses of this is huge.  Sure, running wires for hundreds of miles is expensive, but wireless power transmission is only about 10-20% efficient if you're lucky.  Invest the money up front for the wires and you'll be saving money later on because you're not wasting as much power on a daily basis.

Even over the past 20-30 years there have been people trying to transmit power wirelessly.  Some people have proposed putting solar panel farms in space and beaming the power down to the ground.  Others have proposed using wireless power to send power from the ground to airplanes, rockets, etc.  These have all fallen flat because it just didn't make economical sense.  

As for sending power into the ionosphere for transmission:  Yes, it's possible.  Basically you create radio waves of a specific frequency and send it at an angle into the ionosphere.  It will bounce off it, and come back down to the ground.  With this it is possible to send radio signals "over the horizon".  Early radio operators used this technique to communicate vast distances -- distances that would not have been possible otherwise.

Technically, if you send powerful enough radio waves it would be possible to power something on the receiving end.  Practically, however, it doesn't work that way.  With this method your efficiency would be abysmal.  Probably less than one millionth of the power would be recovered at the far end.  Further, the weather in the ionosphere will affect how well things bounce.  Early radio operators might go long stretches of time when communication between certain cities was impossible until the weather changed.

Conclusion:

It certainly seems that anything useful that Tesla did is already understood by scientists, and anything that is practical to be exploited has been exploited.  Anything that remains is not useful/practical/economical.

Further, anyone who claims otherwise should be treated with a healthy dose of skepticism.  Not all of them will be crackpots, but many of them will be (or at least lacking in scientific understanding).