It's possible, yes.
M193 is probably the best choice for an all-around ammo selection, given its low price, wide availability, and the ability to be stabilized from any 5.56 rifle. For military-type operations, M193 should comprise the bulk of your 5.56mm ammo. However, other types of ammo may be better for a specific application, such as home defense or police work, or when using a 5.56mm gun with a very short barrel or when velocity is likely to be low.
For police-type work where a soft-point is desired, Winchester's 64 grain PowerPoint (in the Super-X line) and PowerPoint Plus (Supreme line) are top performers.* It has the advantage of being less sensitive to velocity by relying on bullet expansion rather than fragmentation, and is more consistent over a longer range of velocities. It would also be a better choice for use in AR-type pistols and short-barreled rifles, where the short barrels impart much lower velocities on the bullets. The downsides of this round are: questionable stability in 1:12-twist rifles, a smaller wound channel compared to a fragmenting bullet, and a cost of 3-4 times as much as M193.
*Note: Winchester offers a crimped version of this load in their LEO-only Ranger line. Stock number RA223T2. This load was selected as the standard duty load by the California Highway Patrol (CHP).
This question really comes down to how much ammo you want to purchase (cost) and how much faith you have in fragmentation (or which side of the fragmentation/controlled expansion argument you come down on). There are strong arguments on either side. The determining factor for you may be small. If you expect engagements inside your home, or under 50 meters, M193 and M855 will perform wonderfully for you. As ranges go out past 150 meters you may prefer heavier hollowpoint or softpoint rounds.
The authors tend to prefer M193 over specialty rounds (with the exception of 77 grain Nosler NATO loadings for special home defense applications) and M855 because we believe it produces larger wound cavities and is more effective at likely defensive ranges (inside 150 meters), as well as easier and cheaper to buy in bulk-- making it cheaper to train with the ammo you use defensively. This is key, because no ammo is going to be effective if you cannot place shots on target.