Is verbal position used to indicate definiteness in modern Mandarin?
In my (long) studies I've never come across a formal definition of &quot;definiteness/indefiniteness&quot; specifically used to describe a grammar rule of Mandarin.
However the phenomenon you are talking about happens in many languages, and can be explained as stressing a certain element of a sentence by means of syntax (i.e. word order).
By rearranging the order of the words, of course within the boundaries of grammar, you can achieve this effect of giving more prominence to some element instead of another.
This happens in other languages as well. For example Spanish is a pro-drop language, so when you do specify a pronoun you are putting extra stress on it:

me llamo Pedro (= my name is Pedro)
yo me llamo Pedro (emphasis on &quot;me&quot;, it's me who's called Pedro, and not somebody else)

In these cases, further implications may exist, otherwise there would be no need to stress a normally unstressed element, right?.
At this point you should also consider that some syntactical constructions, which are widely used in Mandarin, have the specific purpose to stress some element of the sentence. Some of them are:

topic-comment, and not just in Chinese!
constructions with 把

Topic-comment
According to some linguistics theories, in the topic-comment structure the comment (or rheme) is the focus of the sentence. The term &quot;focus&quot; is technical and means the new, non-derivable information that is said about something (the topic).
Hence it follows that the topic is known, derivable information. So when you topicalize something, you imply that it is known, and that's why it can take the definite article in English:

人来了 (topic = 人 = known information; comment = 来了 = new information)
&quot;the (previously stated) person(s) have come&quot;

The other example 来了人了 doesn't topicalize 人, so it doesn't imply that 人 is known: &quot;some person(s) have come&quot;.
Constructions with 把
It's easy to make sense of your given example if you consider that 书 in 买书 has a non-specific meaning. This frequently happens in Chinese with separable verbs, where the objects contribute meaning to the verb instead of representing an actual target of the action. E.g. 我想吃饭 I want to eat food. Those are some times called virtual or ostensive objects.
So in 我在买书了 the object 书 is non-specific, and in English you can use the plural &quot;I'm buying books&quot;.
Objects that can be extracted with 把 need to meet certain requirements:

The direct object of a bǎ construction [...] is usually definite, meaning that it is specific and unique (as in phrases beginning with the equivalent of this, that, these, or those).

So the sentence 我把书买了 implies that 书 is known and definite, therefore it translates as in your example &quot;I bought the (previously talked about) book&quot;.

In conclusion:

Is verbal position used to indicate definiteness in modern Mandarin?

No, not verbal position. It's the position of the element whose definiteness/indefiniteness shifts following different syntactical constructions.