I think it is a fairly good possibility that George and Charles were brothers given that they seem to have been sharing the same address in Looe Street. If that is the case then knowing about Charles, gives you information about George that you didnt have before ie. born in Plymouth to father named William (a carpenter). Unfortunately early baptisms will not state the fathers occupation. But if you find baptisms for both a George around 1802-03 and a Charles around 1810-1811 with the same parents, then you might feel confident you have the correct ones. Be prepared to consider various spellings.
As you say, NO baptisms for either George and Charles have been found, but there do seem to be gaps in the records. For example, I could see burials in Charles the Martyr, Plymouth, but not baptisms for the time of interest. In my experience FindMyPast has the best coverage of Devon records so I would try to see what records you can access there. Using FamilySearch, Ancestry and FreeReg, I could find no relevant baptisms.
----------------
I did some work on the witnesses to both marriages today, as often these turn out to be blood relations and can be important leads - apart from Eliza Hawkins.
William Blight UNDERHILL was born 1812 Plymouth. His parents Hugh and Grace were residents of Looe Street.
Ralph RYDER/ RIDER was born 1797 Modbury Devon. He was a cabinet maker & his father Ralph was a mariner
Ralph Married Mary STONEMAN abt 1823
In 1841 living in Charles the Martyr Plymouth (Jubilee St)
In 1851 living in Charles the Martyr Plymouth (Salem St)
2nd wife jane PEPPERELL (married 1839)
Robert LEWIS was born abt 1804 Plymouth. He was a stone mason & his father was a builder.
Robert married Georgiana BOWDITCH 1829 Plymouth
In 1841 living in Charles the Martyr Plymouth (North St)
In 1851 living in Charles the Martyr Plymouth (Green St)
----------------
Just a note for future reference - Charles says his father William Hawkins carpenter
There is a William Hawkins in the Plymouth workhouse in 1841 (age 65 born abt 1776) and a baptism for him 1776 in Charles the Martyr. No way of knowing if this William is of interest at this stage.