access to voice messages without cellular access?

I would put a personal greeting on my voicemail to indicate "I'm unable to receive voicemail at present--if you need to contact me please do so by Text or by Email". Most voicemail systems allow you to make just an Announcement without even allowing your caller to leave a recording--that's probably best to do.

And instead of Airplane mode just turn voice roaming Off, as well as cellular data, under Network prefs.

You can turn cellular data off in settings, and a trick I've used in the past, is to forward my calls to a number that has no answering machine, like my home landline. That way, if anyone does call you, the calls will not come through to your phone, nor will they be picked up by your carrier's voicemail. That way you can avoid putting the phone into Airplane Mode & use GPS without fears of nasty surprises.

Cellular voicemail is stored on the carrier's network and requires a cellular connection.

(unless you have a seperate voicemail set up in your Skype account or other VoIP service)

if your carrier allow for you to access the voice mail on the Internet otherwise no

Unless these were calls telling you that you just won a million dollars or so, you don't want to listen to the messages anyway, as it will cost you a million dollars or so just to listen to them.