In the past 20 years I have traded odd and mixed lots many, many times and I have never not had an order filled in toto if NBBO size was larger than my order. It may be because my broker offers Smart Routing but I can't state that this is true across the board. Here's the information that they provide for traders:
An odd lot is a number of shares less than 100 (1-99)
A "Round Lot" is 100 shares of stock
An order for a number of shares greater than 100, but not a multiple of 100 (i.e. 142, 373, 1,948, etc) is a "Mixed Lot" (AKA PRL, or partial round lot, order)
Odd-Lot orders are not posted to the bid/ask data on exchanges
Odd-Lot orders are taken into the order book at the exchange they are routed to. When the exchange is able to match an order from the other side of the book with the odd-lot, it will be filled. This could lead to delay on execution of an odd-lot.
There are numerous guidelines for the routing of odd-lot orders:
Odd-Lot orders to initiate positions will not be routed to primary exchanges; Odd-Lot orders can be routed to primary exchanges, but only if the order in question is to close out a preexisting position; IB will not direct-route odd-lot orders which initiate positions to primary exchanges, therefore these type of orders should be Smart Routed so that IB's routing system can send the order to an ECN for execution. The exception is that odd lots can be routed to NYSE/ARCA/AMEX, but only as part of a basket order or as a market-on-close (MOC) order.
A mixed lot or PRL (i.e. 257 shares) direct-routed to NYSE/AMEX will be submitted in whole to the exchange (applies to both market and limit orders). If the order is direct-routed to NYSE/ARCA, only the round lot portion of the order will be submitted and, if it is executed, the IB system will cancel the remaining odd-lot portion of the order. If the order is routed via IB Smart Routing, all market centers are eligible to receive the order according to the Smart Routing logic (including NYSE/ARCA, but only for the round lot portion of the order).
IB will not route odd-lot orders for HOLDRS. The odd-lot portion of a PRL order for HOLDRS will be rejected by the IB system after the round lot portion of the order is executed.
Individual exchanges may impose certain restrictions on odd lot orders, in addition to any of the restrictions mentioned above
As you can see, there's no one size fits all answer, well, at least at my broker.