tl;dr: Use separate fields for the type and a GUID-only ID and use hash indexes on both.
This answer is necessarily going to be somewhat opinionated based upon the nature of your questions. Let me first address what appears to be your primary concern, namely the fragmentation of indexes effecting performance.
DocumentDB assumes the use of GUIDs and a hash index (as opposed to a range index) is ideally suited to finding the one matching entity by GUID. On the other hand, if you want to find a set of documents by looking at the beginning of the string, I suspect that would probably be more performant with a range index. This assumes that STARTSWITH is only optimized when used with range indexes, but I don't know for a fact that it is optimized even when you have a range index.
My recommendation would be to use separate fields for the type and a GUID-only ID and use hash indexes on both. This gives you the advantage of being assured that queries like the one you show would be highly performant and that queries which combine a type clause with other parameters would also be able to use at least one index. Note, hash indexes of this type (say 2x 3 bytes = 6 bytes/document) are highly space efficient, so don't worry about needed two of them. Those two combined should be much smaller than one range index which needs to have enough precision to cover the entire length of your type+GUID.
Other than the performance and space reasons already discussed, I can see a couple of other disadvantages to combining the type with the GUID: 1) when trying to retrieve a single document (both for direct use and as part of a foreign key lookup), having the GUID separate and using a hash index will be faster and more space efficient than using a range index on the combined field; 2) Combining the type with the ID greatly complicates certain migrations that commonly need to be done at a later date. Let's say that you decide to break your users into authors and readers for example. Users are foreign key referenced in other document types (blog post author, reader comment, etc.) by the user ID. If that ID includes the type, then you would need to not only change the user documents to accomplish the migration but you'd also need to find and change every foreign key. If the two fields (GUID and type) were separate, then you'd only need to change the user documents. Agile software craftsmanship is largely about making decisions that provide flexibility down the road.
As for the use of a sequential index, the trend in databases in general and NoSQL in particular, is that the complexity of providing a monotonically increasing sequential ID is greater than the space-efficiency advantages of that over a GUID. If you are going to stick with DocumentDB, I recommend that you just go with the flow and use GUIDs.
