Yes, he could have done, though probably fresh water, since that's what would have been available from the Tiber- we have references to the diversion of these waters to pools for these spectacles in the works of a civil engineer, Sextus Julius Frontinus

In the ancient world the practice of staging naumachia -- sea battles -- for entertainment is well attested. We have references to such spectacles staged by Caesar and Claudius as well as Nero.

As to the animals provided-- we've got evidence of entrepreneurs and the military scouring the Earth for animals to entertain Roman audiences, and we've got references to astonishing numbers of animals used:

in 55 BC Pompey gave venationes with 600 lions, 410 leopards, some apes, a lynx, a rhinoceros and twenty elephants (Cassius Dio XXXIX, 38, 1-4; Cicero, Epistulae ad familiares VII, 1, 3; Pliny, Naturalis historia VIII, 7, 20-1). At Probus' venatio in AD 281 more than 3000 ostrich, deer, boars and other herbivores, 400 big cats and 300 bears were killed (Scriptores Historiae Augustae, Probus 19, 4-8). The largest number of animals killed was some 11,000 over 123 days at Trajan's triumph in 108-9 BC (Cassius Dio LXVIII, 15, 1).

While bearing in mind that we've got no way to verify these numbers, and that there's lots of reason to imagine exaggeration-- it's also clear that Romans liked this kind of entertainment. Rome's appetite for animals is considered responsible for the depletion of several lion populations.

The reference to seals and polar bears is likely is coming from Calpurnius Siculus:

aequoreos ego cum certantibus ursis spectavi vitulos

. . .and that's not really specific as to species. I'm also a bit skeptical because when the Romans had a really unusual animal, there's a lot of discussion about it. Martial and others discuss the rhinoceros, which made a real impression and appears on one of Domitian's coins. If they'd really had a polar bear (maybe traded by Germans from Norway?) and it had survived the journey to Rome (unlikely) I'd have thought it would have gotten more attention. We have some evidence for specialized lion and bear hunters, they'd have known if they had something unusual, and have gotten a premium price for it.

I might also mention that Tacitus records one of the more spectacular episodes of Nero’s debauchery, also set in a pool, in the Annals. Tacitus is generally considered a solid source, and if you believe any of what he says to be true, then Nero was not only staging naval battles, he was partying very hard in the pool.

See:

Taylor, Rabun. “Torrent or Trickle? The Aqua Alsietina, the Naumachia Augusti, and the Transtiberim.” American Journal of Archaeology, vol. 101, no. 3, 1997, pp. 465–492.

Lindstrøm, Torill Christine. “The Animals of the Arena: How and Why Could Their Destruction and Death Be Endured and Enjoyed?” World Archaeology, vol. 42, no. 2, 2010, pp. 310–323.

Coleman, K. M. “Launching into History: Aquatic Displays in the Early Empire.” The Journal of Roman Studies, vol. 83, 1993, pp. 48–74.

Townend, G. B. “Calpurnius Siculus and the Munus Neronis.” The Journal of Roman Studies, vol. 70, 1980, pp. 166–174.

Deane R. Blackman and A. Trevor Hodge. Frontinus' Legacy: Essays on Frontinus' "De aquis urbis Romae." (University of Michigan Press, 2001)

Epplett, Christopher. “The Capture of Animals by the Roman Military.” Greece & Rome, vol. 48, no. 2, 2001, pp. 210–222.