NON-Random UUID keys in custom distributed DB
Yes, you can use a sequentially generated UUID as a primary key.  SQL Server even has it built in:

CREATE TABLE dbo.keytest
(
    kt_guid uniqueidentifier NOT NULL
        CONSTRAINT keytest_pk
        PRIMARY KEY
        CLUSTERED
        CONSTRAINT keytest_kt_guid_df
        DEFAULT (NEWSEQUENTIALID())
);


Insert some rows, and SELECT them:

INSERT INTO dbo.keytest DEFAULT VALUES;
GO 10

SELECT kt.kt_guid
FROM dbo.keytest kt


Results:

╔══════════════════════════════════════╗
║               kt_guid                ║
╠══════════════════════════════════════╣
║ D9A1905A-ADBE-E911-9440-005056805C06 ║
║ DAA1905A-ADBE-E911-9440-005056805C06 ║
║ DBA1905A-ADBE-E911-9440-005056805C06 ║
║ DCA1905A-ADBE-E911-9440-005056805C06 ║
║ DDA1905A-ADBE-E911-9440-005056805C06 ║
║ DEA1905A-ADBE-E911-9440-005056805C06 ║
║ DFA1905A-ADBE-E911-9440-005056805C06 ║
║ E0A1905A-ADBE-E911-9440-005056805C06 ║
║ E1A1905A-ADBE-E911-9440-005056805C06 ║
║ E2A1905A-ADBE-E911-9440-005056805C06 ║
╚══════════════════════════════════════╝

In fact, in situations where good insert performance is desirable, it may be more effective to use sequential GUIDs instead of randomly generated ones.  Sequential GUIDs make great keys since they are monotonically increasing, which reduces unnecessary page splits when inserting rows into the index.