Charlie, your destination is unclear but it appears you are talking about Mt. Washington. I wouldn't venture above treeline if the weather is poor. Whiteouts can be disorienting for anyone, especially beginners. A refreshing walk in the rain in the woods can turn into a life struggle above treeline. I do recommend trekking poles for your descent. Good luck! and welcome to Summit Post!

I agree with Bark Eater. Above treeline on a bad-weather day in late June, you're looking at temperatures in the forties. Combined with wind and rain it's not just miserable, it's life-threatening - worse than winter in some ways. Throw in a risk of getting lost in the fog and it's just not a good idea.

The Jewell trail is an easier and safer ascent route than some others, but it's not a direct route to the top. It hits treeline on a shoulder of Mt Clay and then follows the ridge for about a mile and a half. You'll be fully exposed to the wind all that time. It's too early to say how strong the wind will be on Sunday, but it looks like a major all-day rainstorm, so I wouldn't be at all surprised to see winds strong enough to knock you down. I'd also expect some hail, which can be painful.

Oh yeah, we don't usually worry much about lightning in the Whites (not compared to, say, the Rockies), but even here, a big storm is no time to be walking along the top of the highest ridge in New England.

What to bring?
-best raingear you can find, including hood, pants, gloves
-warm clothing, including hat
-changes of clothes (shirt and socks, at least), packed in a waterproof bag
-tarp for emergencies
-compass, map, some training in using them (don't count on GPS in a storm!)
-knowledge of the symptoms of hypothermia, and an agreement to check each other frequently and that either party can call for an abort at any time.
-enough common sense to turn around BEFORE you lose track of the trail

(Finding the summit is easy: just go uphill. Finding a safe way down again is the trick.)

If your partner is proposing to hike up given Sunday's forecast and is not telling you VERY firmly to bring warm and waterproof clothing from head to toe, find another partner!

Trekking poles are good for any kind of hiking endeavor. I wouldn't go anywhere without them.

Eh, trekking poles are another question. They can be helpful, but they can also slow you down. Instead of just looking for places to put your two feet, now you're looking for four secure placements with every stride. On tricky terrain you go much faster without them.

On normal trails they're great when you've got poor balance due to a heavy pack or bad snow conditions, and they can take some strain off your legs if that's an issue for you, but I'd almost never say they're "needed".
Luckily, they don't weigh much, so you can try them for yourself, and just not use them if you find them getting in the way.

I never thought trekking poles had much value for me until a couple of years ago. I find my balance becoming poorer with advancing age. Not uncommon. On steep trails and class 2 scree they definitely help my confidence level on the descent...not sure if I move any faster. If I get to class 3 and are scrambling a lot and looking for handholds they just get in the way.