Other than for a very brief time at low rpm and low load it certainly wouldn't. If it were sufficient then that's how engines would be designed rather than at the 30 to 70 psi range that most fall into.
Little ends take the same load and that's a rocking motion, and they
Well they don't carry any of the rod's weight and inertia, just the piston's, but it's an interesting point and frankly one I haven't looked at in full detail before. The metallurgy is different from that of a very soft white metal shell bearing and they can't generate a hydrodynamic wedge oil film because it isn't full rotational motion so pressure feeding wouldn't achieve much anyway. Instead they rely on very minimal running clearance, usually a sliding fit, so that contact point loads are avoided.
Lawnmower engines manage with big ends that are splash, or scoop, lubricated but they also use aluminium as the bearing material rather than white metal and the rpm and loadings are fairly low.
A bearing that relies on a hydrodynamic wedge oil film needs a running clearance, by definition, in which this film can be generated. Normally between 1 and 3 thou radial clearance. If the oil film breaks down then you get point contact, very high pressure loadings and consequent failure. You need a certain minimum oil supply pressure to allow the hydrodynamic wedge to form. This supply pressure is a function of load, speed and clearance. However a bearing that uses sliding fit running clearance also spreads the contact loads over a fairly large surface area all around the pin which obviates the need for a high pressure oil film to avoid metal to metal contact in one particular spot.
The other feature of little ends is the very high surface hardness and high polish of the pin so as to minimise friction and wear and maximise the difference in surface hardness between the pin and the housing. Tribology is complex but in general bearings work best when the two materials in contact aren't of similar hardness. Cranks on the other hand can work fine with unhardened journals because there is no metal to metal contact anyway under ideal conditions. If you tried to design a little end with unhardened pins and non zero running clearance it would fail very quickly.
-- Dave Baker - Puma Race Engines