Competitive in the same sense that the 109G-6, or the D11, or the Mossie can be competitive. They need a chance, but given a chance, they can be dangerous. The primary only weakness would be the guns.
Not remotely as competitive as those. Last I checked all of those maintain positive kill/death ratios, something I highly doubt the Tiffie Ia would do. Anything that maintains a positive kill/death ratio is either good or favored by a small group of elites who distort its numbers. .303s require you to stick to your target, not something the Tiffie is good for. All three of the aircraft you mentioned have good to great firepower, and in the case of the Bf109 good handling as well. Firepower matters. I remember more than a decade ago Citibria, IIRC, trying to use each fighter then in inventory and maintain a 5+kill/death ratio with it. The only one he could not do so in, and it wasn't even close, was the C.202 as it just didn't have enough firepower. This was before the Spit I and Hurri I were added.
I am not saying it wouldn't get kills. I've bagged two single engined fighters and one twin engined fighter just using the four .303s on the Mossie, but I certainly wouldn't recommend it. Nothing using just .303s is competitive.
The other problem with the Typhoon Mk Ia is that it wasn't used because the Hispanos didn't fail. It was merely planned as a backup in case the Hispano cannons proved to be non-viable air-to-air weapons.