I found a solution, but it's a slapped together hack. I'll post it just so someone trying to do the same thing at least knows it's possible.
What I have been trying to do is place an Adsense block in a left-hand column using the mac_ox_x theme. If I had placed the block in the right-hand column I wouldn't have had any issues, but I am stubborn. If I were to place the block in the right-hand column, the variables for the page content (or lack thereof) would have been parsed and available to check for the Adsense column, but trying to place the ads before the info was available created an unique problem. This problem will also exist for those trying to place an Adsense block as a custom header.
Having ads not display on the search page, search results page, login pages, and while in admin mode consisted of checking some predefined variables,
empty( $_POST ) // the post variable will be passed on a search result, so if it is empty, show the ads
GALLERY_ADMIN_MODE // determines whether or not you are in admin mode, this way you can check ad content by simply switching to user mode
$_SERVER['PHP_SELF'] == 'index.php' // show ads on index.php page
$_SERVER['PHP_SELF'] == 'thumbnails.php' // show ads on thumbnails.php pages
$_SERVER['PHP_SELF'] == 'displayimage.php' // show ads on displayimage.php pages
This didn't stop ads from showing on "No image to display", message, or error pages.
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Warning, this is how I did it, the implementation is terrible and just thrown together. It's just a reference for those curious as to how I did it.
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init.inc.php - added the $adsense variable and set it to "0"
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg375.imageshack.us%2Fimg375%2F3892%2Fstep1vl8.gif&hash=98a21fdd3c356b2385af9a1c83a9b218c811a204)
functions.inc.php - First make $adsense variable global for function. If the "display_thumbnails" function calls the "theme_display_thumbnails" function, set $adsense variable to 1.
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg148.imageshack.us%2Fimg148%2F1329%2Fstep2ow1.gif&hash=72b4b745f85fabb650ebebb6731c34d4848f51cd)
displayimage.php - Set adsense to 1, set it back to 0 if there is any error in the next step.
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg502.imageshack.us%2Fimg502%2F2150%2Fstep3bp7.gif&hash=84f362a76d66f30f75873b443e804370d973d355)
functions.inc.php - Make the $adsense variable global, and set it to 0 if the cpg_die function is called. This should disable the ads for any errors that might happen when viewing "displayimage.php".
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg404.imageshack.us%2Fimg404%2F5659%2Fstep4ut0.gif&hash=32221d017de0e89404ee6e7db10bf5f532987f73)
themes.inc.php - Make $adsense global. Check previously mentioned conditions + check to see if $adsense variable is equal to 1. Add $adsense into template array.
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg166.imageshack.us%2Fimg166%2F8308%2Fstep5wy8.gif&hash=7330fc7726a971270f154654812444fa7afc26d4)
template.html - Define ADSENSE_COLUMN variable above </head>. Reference ADSENSE_COLUMN variable in empty div. Add javascript above </body> that will modify the javascript ADSENSE_COLUMN variable with whatever code you inserted into the php $adsense variable.
(https://forum.coppermine-gallery.net/proxy.php?request=http%3A%2F%2Fimg87.imageshack.us%2Fimg87%2F8125%2Fstep6ep2.gif&hash=327ec431bbe1cf0629a0a5b23b5b6adcfc281e98)
Do not add the slashes (\) in the docuemnt.getElementById line, I used php for my template and had to escape the '.