The other two people are describing situations that use the same vendor's equipment at the service provider end and with the exception of a few vendors are on the same device. And at your end must be able to run some version of Link Aggregation Group (LAG), or Teaming, or Multilink trunk. I have worked with many vendors' equipment and some vendors will work with one vendor at the service provider end and another vendor at the client end, but none of them will work with different vendors at the service provider end or at the client end. The problem is that they do not all follow the standards exactly, but interpret them to allow apparently random load balancing between the links. But they do use an algorithm to determine the method of load balancing, and unless they are identically the same, then it will not work.
To provide LAG there must be communication between the devices that look after the two links. Two different service providers using different vendor's equipment simply are not able to do that, and even if they used the same vendor's equipment they would not allow another provider to control part of their network.
You will note that normally the connections must reside on the same device at both ends. Unless you are using very high end routers. The next thing is that the computer would have to set up LAG, or SMLT, to the two routers and you would have to get the two routers to set up LAG to the two service providers.
Normally computers will always use the highest speed connection, which means that it will use the wired 100 Mbps connection rather than the 54 Mbps wireless connection, if you are using G type routers.
So essentially as long as the wired connection is there, the computer will use the wired connection, if the wired fails then the wireless will take over.
So basically you have to have a lot of things in your favour to make it work.