Wallabing
A very original and interesting question! The answer is simple; NO it would put no more pressure on the magazine tube than if the magazine cap was tight against the barrel band.
The lockup points and path of recoil energy for the 870 are the locking block at the top of the breech bolt (it locks the bolt to the barrel) and action bar lock holding the breech bolt carrier and hence the for end assembly in the forward (firing) position. Most all of the energy transfer from the ignition of a shell is captured and transferred thru these points to the receiver then the stock and then your shoulder. There is some energy transferred forward that of the shot and its cup traveling down the barrel, how ever this is slight and if the barrel is properly locked up it exits the barrel with the projectile. WHAT the magazine cap does DO is to hold the barrel against the receiver stops so the that the locking block can engage the locking lug in the barrel extension and the magazine cap retains the magazine retainer, spring, follower, and shells in the mag tube.
SO, what would happen if you did as you suggest? My thoughts are
1st you would be searching a yard or two down range for the internals of you magazine tube that ejected forward, good luck finding the retainer.
2nd most likely the barrel would move forward upon chambering a shell to the point where the locking block would not engage the locking lug, this condition would automatically lock the firing pin in place and your 870 would not fire (one of the three internal SAFETY features built into the design by Remington). Even if the barrel and breech bolt locked up, the gun would fire as normal.
Most everyone has fired a 870 with the mag cap loose, it is common and does no damage to the scattergun. Some of my time as a trainer of the fine art of “fighting scatterguns” was spend reminding folks to “check the Nut” during long firing sessions and it is also a very good idea and one of my check list items when picking up a 870.
Good Luck & Be Safe