Is MongoDB _id (ObjectId) generated in an ascending order?

_id: ObjectId(4 bytes timestamp, 3 bytes machine id, 2 bytes process id, 3 bytes incrementer)

This is the id structure. So only last 3 bytes will increment uniquely. So the answer of your question is yes.

For mongo version >= 3.4, the Objectid generation is changed a little. Its structs are:

• a 4-byte value representing the seconds since the Unix epoch,
• a 5-byte random value, and
• a 3-byte counter, starting with a random value.

So the first 4 bytes are still the seconds since the Unix epoch, it is still almost ascending but not strictly.

https://docs.mongodb.com/manual/reference/bson-types/#objectid

No, there is no guarantee whatsoever. From the official documentation (at the time of the original answer):

The relationship between the order of ObjectId values and generation time is not strict within a single second. If multiple systems, or multiple processes or threads on a single system generate values, within a single second; ObjectId values do not represent a strict insertion order. Clock skew between clients can also result in non-strict ordering even for values, because client drivers generate ObjectId values, not the mongod process.

And from the latest docs

While ObjectId values should increase over time, they are not necessarily monotonic. This is because they:

Only contain one second of temporal resolution, so ObjectId values created within the same second do not have a guaranteed ordering, and Are generated by clients, which may have differing system clocks.