Yes, it is possible, but you will have to be in debug mode, which means you won't be able to play multiplayer or make any level progress. Here's how you do it.
Go to your AvP Classic folder. The default directory is: Local Disc:/GOG Games/AvP Classic. Locate the file called Launch Aliens vs Predator Classic 2000. Right-click it. Go to Properties. At the Target line, type in -debug after the last quotation mark of the target destination. Click Apply at the bottom and then OK. See the first screenshot attached to this post to see an image of this.
Next, open up your game. You will now be in debug mode, meaning you can alter some of the game's features, but you will not be able to play muliplayer in this mode. Go to the single-player level of your choice. Open up the console (default is ~). Delete SAY. Type in LEANSCALE 0 and then hit Enter. This will disable all leaning. Hit Enter again. Now you can play the level without any leaning. Check the second screenshot to see an image of this.
You cannot make any level progress with debug mode on and you can't save, either. To counteract this, you can
download a completed profile, which will already have all the levels unlocked so you can just play straight through the missions with leaning turned off.