" Signify have said they will be stopping support for the 1st gen bridge and switching off online services for this on the 30th April 2020"
So if they kill online services for the gen 1 bridge, will Hubitat stop working with the bridge or is the integration local and not cloud dependent?
No, Hubitat's integration is entirely local and will keep working. (I would not be using Hubitat if it weren't, that's for sure.)
Philips/Signify is just ending cloud service support, as you mentioned, for the Gen 1 Bridge. This is mostly things like MyHue for away-from-home control via the app/Bridge, plus whatever Internet-only services you might have it tied to like IFTTT.
So if my hue bulbs are connected to my hue gen 1 bridge and I'm using the hue integration app, rather than my hue bulbs paired directly to hubitat, is this relying on the cloud? Or is hubitat talking to the hue bridge locally?
No, as I mentioned, the Hue Bridge integration from Hubitat works entirely over your (local) LAN. This will continue working indefinitely just as it currently does. Even the Hue app itself works locally if you're on the same LAN, so it's just the remote (and cloud) features that this affects.
You can test this yourself if you feel adventurous: disconnect your Internet but keep your LAN up (e.g., with a DSL or cable modem, you can disconnect the phone line or coax cable), and watch how it still works. 
Awesome! Good to know! On that note, what would be the pros and cons of connecting the hue bulbs directly to the hubitat hub rather than the hue bridge?
There are mostly cons. These issues are well-commented on in the forum (both here and many others) if you search, but basically, they're bad repeaters for non-bulbs and are likely to cause problems unless they're the only kind of Zigbee device you happen to have. (There's a small mention of this in the documentation, too: How to Build a Solid Zigbee Mesh - Hubitat Documentation)
Beyond that, the only cons are that you'll lose access to some Hue features, like default power-on state, "true" scenes (Hubitat has a scenes feature but there's no comparison to on-bulb Zigbee scenes), the ability to use Hue accessories (like the Tap and Dimmer, though the latter could also be made to work with Hubitat), and so on. If you had a v2 Bridge, you'd also get native HomeKit/Siri support that both v1 and Hubitat lack (and v2 gets you color control via voice assistants, which Hubitat also supports).
Oh yes, the zigbee bulb repeater problems! Definitely well commented on now that I think about it. Well it's pretty cool that Hubitat will prevent me losing cloud control over my hue bulbs if I wasn't using hubitat. I would have had to upgrade to a 2nd generation hue bridge which probably would have cost me the same, if not more, than the hubitat hub!
Edit: just checked and the hue gen 2 bridge is $70CAD and I paid $95CAD for the hubitat hub so I'm pretty happy with that!
I never thought of it that way and was initially confused (Hubitat won't restore Hue's own cloud connectivity), but if you consider Hubitat's cloud dashboards and whatnot (which will continue working), then that is certainly one advantage. 
In the US, I think it's around $50 USD for a new Hue Bridge or $80 USD at Hubitat's current price--and I see a refurbished Bridge for under $38. I'd still probably get the Hue Bridge if I was only using it for lighting--"true" scene support and group messaging that you don't have to think about are amazing to have. But with HubConnect or HubLink/Link to Hub, either would certainly work! (Or you can keep using the gen 1 until something breaks 
)
So does the Hue Bridge need registering? If they shut down does that mean that you won't be able to register new hubs going forward? Would it be worth buying now just to register it?
The Bridge doesn't need an Internet connection at all--it will come preloaded with some firmware version, and all hub discovery and setup can be done entirely over your LAN. That being said, you may want one for firmware upgrades (they haven't released one for the v1 Bridge since February of 2018 and will likely never do so again, but you might be able to get updates for bulbs/accessories, not that I think there have been any noticeable changes/fixes for their use with a v1 Bridge...and if you buy a used Bridge, who knows how long it may have been offline). After that, though, without their cloud features, I guess it would be as good without Internet as with it...and maybe a little better given that it will be running an outdated OS.
Thanks. I really don't have a need for this, other than maybe if I decide to do a few more smart bulbs. Most of my stuff is smart switches, or dedicated LED controllers.
It pays to wait sometimes (iris) and sometimes you get orphaned devices that are worthless. It sounds like I will be OK to wait and IF I need the Hue Bridge, I can pick one up on ebay cheap later on. Future bargain in the making.
I can confirm that my Gen 1 Bridge recently offered a firmware update for at least one of my hue bulbs and one hue remote. so, for now, although the gen 1 bridge isn't getting updates, the bridge is still offering updates for bulbs and remotes.
For $33.99 you could solve the issue of Gen 1 not receiving further updates 
Download the Hubitat app
