Those who deal with vintage Macs regularly (I do but had to learn from the best) tell me a 17-inch VGA monitor will work if it supports H-sync, V-sync, composite sync and sync on green, which half of the cheap 17-inch VGA monitors did (if yours does not, the adapter won't drive it.) If it IS compatible however, with all four types of sync, it will work on either the IIci built-in video (for you) or IIcx Radius Two-Page Display video card. I know this because from a thrift store I got a Samsung SyncMaster 731N LCD monitor that supports all four types of sync and it works on the IIci built-in video despite being even newer and using CCFL backlighting TFT LCD technology. It's not supposed to work, but it does with an Enhance Liberty Adapter Mac to VGA the monitor you have should work and the Samsung SyncMaster 731N for sure will work (even the Radius Two-Page Display card despite not using color it winds up having a pin that does the same thing as sync on green and all the other sync categories directly transfer over.
The thing the OP needs to remember is he needs to get the Samsung SyncMaster 731N because unlike you he doesn't have a monitor compatible with the graphics card on his IIcx. If he upgrades to a IIci the Samsung SyncMaster 731N will allow him to use the on-board video equally well with the adapter I put in bold because of the fact it supports both the same resolution as the AppleColor High-Resolution RGB monitor and the 1152x870 resolution of the Radius Two Page Display video card-it's a multisync monitor that supports all the peculiarities of Mac II single-resolution graphics.
I love doing vintage desktop publishing on my IIci and I've got a Radius Two-Page Display card of my own oncoming to post pictures of how you can swap back and forth.