can it increase heath/mana

Nurture boosting doesn't affect how the stats increase, it just makes sure the pet is at the front of the nurture pack and gives two scales (which means it's more likely to get more nurtures, but it doesn't affect it in and of itself)

Nurturing can increase HP and Mana, but mana only increases if the pet is maxed in all the other stats.

HP increases when it's the 'lowest' stat, and increases by 20 (I'm pretty sure it's still 20?)
By 'lowest'- A pet with 400 mana is counted as '40' against the other stat, a pet with 800 = '80'
(I think 1000hp-1099 counts as '100' and then 1100 rolls around to counting as '10'?)

(since HP goes up by 20 a pet with 460 becomes a pet with 480, so if the pet was 460hp / 46s / 47i / 48d /47a, you would get 460 > 480 hp, then you'd need +2s, +1i, and +1a before you'd roll around to hp again)

?? yes, they sure are? I am not sure what this has to do with the question though if we could get a clarification

i was wandering if the hp/mp would go up if i nurtured booted them

well, as said, nurture boosting isn't what does anything, it's the people nurturing them. Also as said, mana ONLY goes up if all the other stats are maxed- 2000 HP, 100str/int/dex/agi. The eggs do not have 2k hp, so nurturing once they hatched would give them HP.
If you used a Prisma philter on them, it might be possible that they could hit 2k hp (and they'd also get mana from the philter.)

5677206 would go from 1,715hp to 1,915, which would mean it would need +85 to reach 2k, +85 would be 5 rounds of 8 nurtures, so 40 nurtures to hit 2k hp if it was prisma'd, and then it would start getting +1 to mana for every 8 nurtures

5677208 would get to 1,895, which would take, what, 48 nurtures to hit 2k?

So, yeah, with enough nurtures you could manage to get them both to 2kHP and start getting some extra mana points on them (so Nurture boost would probably help, sure, you wouldn't need to ask people to nurture them as much)