Mining does not require lots of bandwidth to connect to most pools...some pools don't allow lower difficulty ranges though(smaller packets)...full blocks are very very large in packet size....as computers can only read binary so a block is many more bits or would require a very large amount of bandwidth to send all of the information in one packet...however....the difficulty of finding a block is measured by the average probability on finding an answer or the requires bits of information to be guessed as an exact hashed match for confirmation...pools send smaller peices of blocks out, they get solved, and put back then the whole block gets turned in...
however every "answer turned in" or "hash" is a potential block answer as well because like bitcoins current difficulty for example is 1,158,240,270,835 which is the number of possibilities for answers (hash matches)
bandwidth of 4G can send 4 gigbytes of data yes but you have to understand how the pinging works when it comes to mining speed...when your computer sends a call out it sends 2 packets, then 4 , then 8, then 16, then 32, then 64, then 128 then 256, etc.....until it times out...then it goes back to the packet size when it did not time out and sends packets in that size over the connection of how ever fast you have..example at my house I have 5 Gigabytes of bandwidth but only 30 megabits /s second download and 15 upload.....on a 100gigabyte Ethernet connection or 5giga byte WiFi.
(Bits = a piece of information Bytes = U unit of Measurement for bytes represented in bytes per second)
it can be misleading from the internet company I know
I can point all my miners tethered through my cell phone to a pool; with no problem as long as I have a decent signal...
Do an Internet Speed test...there is one on google that pops up when you search "internet speed test" and its very accurate...as long as you have an okay upload of 6-10mb/s or higher then you shouldn't have any problems connecting to pools. Unfortunate though that if you have a 30 Mb/s upload and a 5 mb/s upload you have an average connection speed on full duplex of 25mB/s.