Apple ID and Podcasts Connect

Short answer: yes.

Longer answer: when you change the email address which forms your Apple ID and thus login to another email address (as opposed to starting a completely new Apple ID) you are not changing the ID, only the 'name' of the ID. ('The name of a thing is not the thing itself' - Umberto Eco.) So you won't have any difficulty with Podcasts Connect, iTunes or iCloud provided you go about it properly - please follow this method:

If your primary address (the ID) is an @icloud.com, @me.com or @mac.com address you cannot change it. If it is a non-Apple address you can change it as follows:

1. Firstly, sign out of iCloud on all your devices: go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server). If you have 'Find My iPhone' etc enabled you will need to disable it first. Your synced data will disappear from your devices but will reappear when you sign back in.
2. Create a new email address, for example  at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it is not associated with an Apple ID). You can change it to another Apple address only if it's listed when you click the link to change (in practice this means your main @icloud.com address, and the equivalent @me.com and @mac.com versions if you have them: it does not include email aliases).
3. Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
4. Where it says 'Apple ID' and gives your current ID email address, click 'Change your Apple ID'.
5. Enter your new address and click 'Save changes'
6. Sign back into iCloud on all your devices with the new ID and password. Your synced data will reappear (give it time).

I reiterate - before you start, sign out of iCloud on all your devices. Failure to do this will lead you into difficulties.