Will deleting WP’s code in .htaccess cause problems?

Adding the [L] flag to the [NC,R=301] piece (ie, [NC,R=301,L]), which tells the RewriteEngine that the RewriteRule is the last one for the block of RewriteConds, apparently solved the problem.

RewriteEngine on
RewriteCond %{HTTP_HOST} name.com
RewriteCond %{REQUEST_URI} ^/(1[0-9]{3}|200[0-9]|201[0-3]) 
RewriteCond %{REQUEST_URI} !/2013/12 
RewriteRule ^([0-9]{4})/([0-9]{2})/(.*)$  http://v2.name.com/$1/$2/$3 [NC,R=301,L]

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

Reference

• Apache’s URL Rewriting Guide and mod_rewrite documentation (particularly the section on RewriteRule)