Does the number of (English) neologisms remain constant over the years, or, as I strongly suspect, does it grow exponentially?
Wouldn’t it be counter to that? The more words we have, the less need for new ones. It’s not like they reproduce, after all…
Portmanteaus are rather randy.
I don’t follow that logic at all. Our society is more complex than 100 years ago, especially related to technology. Plus, slang is constantly being created, and sometimes making it into mainstream speech.
I suppose you could count the lists of new words added to the OED from one year to the next, but I lack the patience to do so.
According to your link, last summer the OED recognized “quantitative easing” as a new word. Apparently I don’t know what “word” means. 
What the OED means are lexical entries. That is, it’s anything that should have a separate entry in a dictionary. Since “quantitative easing” means something that’s not obvious from the words “quantitative” and “easing,” it’s a separate lexical entry.
I expect that the number has grown, but not exponentially.
I don’t see any good way of establishing this, though. Dictionaries do have editors that look for new words, but historically they have depended on a legion of volunteers who sent in examples. Obviously the more eyes looking at more diverse work the better.
Word finding hasn’t been consistent. There were times when more people were more actively involved and periods - wars, for example - when there were fewer. Where to look for words also has evolved. Early dictionaries concentrated on literary fiction and essays as sources. The OED always had huge difficulties finding people who were knowledgeable about specialized and technical vocabularies. Slang was usually avoided, as were vulgar terms.
We look at many more sources of word formation than ever before. And there are physically many more places to write out words. That has more of an effect than sheer quantity. Words only make it into the dictionary when they are used regularly over a period of years. The more places to write words, the more likelihood that they will stick and be found over a period of time. It’s impossible to know how many words were coined in the past that had fleeting lifetimes, few uses, or appeared in places not consulted.
It gets worse. What is English? The OED had huge controversies over including Americanisms. The editors did include some terms from Indian-English and Canadian-English and all the other Commonwealth Englishes, not to mention Scottish, Irish, and Welsh Englishes, but was never comprehensive about them. In today’s world, where English is the common tongue, there must be many terms Americans rarely see, but that was also true in the past and there’s no way to determine to what extent.
So the recorded number of neologisms may be vastly higher, but the base is surely wrong to possibly an order of magnitude. There’s no one-to-one correspondence to measure from.
These folks said it better than I can - 
The problem with defending the purity of the English language is that English is about as pure as a cribhouse whore. We don’t just borrow words; on occasion, English has pursued other languages down alleyways to beat them unconscious and rifle their pockets for new vocabulary. - James D. Nicoll -
English is the result of Norman men-at-arms attempting to pick up Saxon barmaids and is no more legitimate than any of the other results. - H. Beam Piper -
Great quotes! 
To be fair, any analysis of the new words must also looks at abandoned words, i.e., those which are no longer being used.
Yes, but as soon as you discuss an abandoned word, it’s being used again. 
The word you’re searching for regarding the theory is dic-doubla-growthfulness.
And also a word which had been classified as “archaic” may turn out to have become a “regionalism” instead, or one of its meanings is archaic while others are in perfect health.
So you’re saying some words have perfectly cromulent uses?
What would that be? random+handy?
Unless its not actually a portmanteau. NOAD defines “randy” as such
1 informal sexually aroused or excited.
2 Scottish, archaic (of a person) having a rude, aggressive manner.
So…ah…portmanteau’s are sexually aggressive? Or rudely excited?
The fact that they’re two words getting it on with each other.