The short answer is 'no'. It isn't actually a synonym, although it is related. Let's call on our Sentinel friends for a little help.
Happily is the adverb formed from the adjective happy, meaning, among other things, fortunate, satisfied, enthusiastic. It comes from Middle English 'hap', which means 'luck'; by chance or accident.
Hap itself comes from Old Norse 'happ'. As a word in its own right, it is now archaic, but survives as 'happen'.
Other words deriving from 'it may hap' (16th century usage), are mayhap, maybe, or perhaps.
Haply is an adverb meaning 'by chance or accident'. A variant of it, spelled happely, dates back to at least 1483, when Caxton used it. At that time it meant 'perhaps', but it could also mean 'fortunate chance', which does connect with happy or happily because 'fortunate chance' could also be worded as 'happy chance'.
This example, however, is pushing the bounds of modern usage. While not actually obsolete, haply is now considered archaic, possibly useable in poetry but not in everyday language. It's better to use 'luckily'.
http://www.thefreedictionary.com/happy
http://www.thefreedictionary.com/hap
http://www.thefreedictionary.com/haply
http://www.thefreedictionary.com/mayhap
The Complete Oxford Dictionary
Happily is the adverb formed from the adjective happy, meaning, among other things, fortunate, satisfied, enthusiastic. It comes from Middle English 'hap', which means 'luck'; by chance or accident.
Blair smiled happily when he caught his first fish. He had done so many things over the years, but this was a first. He had never before gone fishing.
Hap itself comes from Old Norse 'happ'. As a word in its own right, it is now archaic, but survives as 'happen'.
By hap, Blair saw what he wanted in the shop window.Today, this would be written as follows;
Blair happened to see what he wanted in the shop window.
Other words deriving from 'it may hap' (16th century usage), are mayhap, maybe, or perhaps.
Haply is an adverb meaning 'by chance or accident'. A variant of it, spelled happely, dates back to at least 1483, when Caxton used it. At that time it meant 'perhaps', but it could also mean 'fortunate chance', which does connect with happy or happily because 'fortunate chance' could also be worded as 'happy chance'.
Jim realized, from the conversation that he was haply overhearing, that the two men were planning a robbery.
This example, however, is pushing the bounds of modern usage. While not actually obsolete, haply is now considered archaic, possibly useable in poetry but not in everyday language. It's better to use 'luckily'.
http://www.thefreedictionary.com/happy
http://www.thefreedictionary.com/hap
http://www.thefreedictionary.com/haply
http://www.thefreedictionary.com/mayhap
The Complete Oxford Dictionary
no subject
14/7/14 19:00 (UTC)In my mind, I connect 'hap' to 'happenstance' -- but maybe that demonstrates that I'm a bit archaic myself. ;)
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no subject
15/7/14 05:13 (UTC)One weird one (not in the 'hap' family) is 'gotten'; it's in my dictionary as archaic; Brits mostly use 'got' - and yet it's still correct usage in America. Because of that, it's regaining a degree of use in the UK. But it's one of the words that I'll write rings around to avoid using in any of my stories. :-)
no subject
15/7/14 15:14 (UTC)Thanks for this post!
no subject
15/7/14 17:15 (UTC)no subject
16/7/14 15:53 (UTC)"Sherlock sighed haply at the Doctor. Dean smiled and haply gave Sam a kiss."
no subject
16/7/14 17:03 (UTC)