And if yes, is it common or rather odd?
Anecdotally, we do see instances of customers buying both our products at the same store.
The Chrome spellchecker doesn't seem to know it, by the way:
I don’t know what you mean by “a proper adverb”.
If you are concerned that it may not be found in this or that dictionary, this means nothing, since derived forms that are generated by productive derivational morphology are never fully enumerated in any dictionary. The absence of a word from a dictionary never proves anything about its validity as a word.
The OED has an entry for the adjective anecdotal and another for the adverb anecdotically. I would rather read anecdotally than anecdotically, as a matter of personal preference.
I think what you are seeing is simply a difference in how Chrome applies derivational morphology, or perhaps fails to do so, within its spellchecking algorithm. Other browsers give different results. So for example in Safari, anecdotally though absent from the OED triggers no red squiggles, but anecdotically in contrast does so, even though it is present in the OED.
I’m therefore guessing this is nothing but a software issue, not an actual English issue at all.
On the other hand, if your concern here is how to analyse it syntactically, then you need to understand that this is an example of a sentence adverb, not an adverb of manner or an intensifier. That means that it applies not to a single verb, adjective, other adverb, or preposition, but rather to the entire sentence as a single syntactic constituent.
What’s happening here is that you have an adverbial adjunct, which in fact is actually a type of disjunct.
Here are similar examples of disjuncts from the cited Wikipedia article:
- Honestly, I didn't do it. (Meaning "I'm honest when I say I didn't do it" rather than "I didn't do it in an honest way.")
- Fortunately for you, I have it right here.
- In my opinion, the green one is better.
- Frankly, this whole paragraph needs work.
- Interestingly, the comment made for a great topic of its own.
- Luckily, the amount of sugar the recipe called for was in stock in the pantry.
- Clearly, the mail did not come today due to it being a national holiday.
- Unfortunately, by the time she reached the bus stop, the bus had already left.
The sentence adverb is clearly a grammatical structure to native speakers, which is about as close to “proper” as you are going to get.