Does my chances for ultra rare increase?

No. It is always a fixed rate of approximately 7,5% per each of the two last slots of Arsenal, Recruit, and Premium Spectre Packs, so it's a 14,4% chance that you'll get a UR weapon per try if you buy these packs. With Spectre Packs, it's just 7,5%, because there's only one slot that can give you UR weapons. That said, Rare Weapons and UR Weapons are in separate pools, which means that getting all Rare Weapons doesn't get you any closer to getting URs more often - for instance, it's been estimated that there's a 72,5% chance (per slot, and there are two) that you'll get a Rare Weapon if you open an Arsenal pack - so the RNG will pull a card from the Rare Weapons pool - or, if this pool happens to be empty, it will use a backup pool (which happens to be Lvl IV Equipment) with the same chance, which is 72,5% per slot, while. again, your chance to get a UR stays THE SAME 7,5% per slot.
BTW, this leads us to the fact that 1 UR should approximately cost 700k credits, so you should get one out of 7 packs you open (if you're neither lucky nor unlucky), but don't be surprised if you spend 2,5 mln and get only Cryo Ammo IV out of there. RNG is so RNG, and its default setting is "screw you", so brace for lots of grind and frustration.

me3tweaks.com/store_catalog/
masseffect.wikia.com/wiki/User_blog:Elseweyr/ME3MP_Store_Guide

if you want more details

Your odds for ultra rare do not change based on what you have already. It is a steady 7.5% per slot that can drop a UR. Maxing out items only changes drops when you close out the pool that is chosen, then the backup pool is selected which contains consumables, basic character cards, etc.