If you get a replacement iPad through AppleCare can you get AppleCare with the replacement?

Any warranty replacement will continue the remainder of the original warranty (including any AppleCare+ extended warranty), or provide 90 days coverage, whichever is longer.

The same, btw, also applies for for-fee out of warranty replacements if they are replaced by Apple or an Apple Authorized service provider.

Apple One (1) Year Limited Warranty

“...A replacement part or Apple Product, including a user-installable part that has been installed in accordance with instructions provided by Apple, assumes the remaining term of the Warranty or ninety (90) days from the date of replacement or repair, whichever provides longer coverage for you...”

Not really. If the original iPad that was replaced had AppleCare+, it will get transferred over to the replacement.

Hope this helps,

Richard