I don't think there could be any question of equality, but we could see a legally established and permanent form of the Gallienic Peace. Decius tends to get painted as a persecutor, but IMO it is far more likely he was oblivious to the Christians than malicious. His edict required sacrifices of all subjects, specifically exempting the Jews as far as we know, and it seems to have come as a surprise to the government how many Christians suddenly appeared prominently refusing to obey. If the Christians had been granbted an exemption similar to the Jews, it is likely they would not have been bothered. Of course Decius was not kindly disposed to them, so it is quite possible he might still have decided to launch a persecution on finding how many there were, but it is far from certain.
As to further-reasching consequences, there could be a lot. Of course there would still be isolated instances of persecution. Christians were likely persecuted before Decius, though it is hard to see how systematic and legal that was. They were not loved by their neighbours, to put it mildly. But locally isolated persecutions would be unlikely to have the same unifying, identity-building effect on the population that the systematic efforts of the 250s and 290s had. The sense of having survived mortal danger together can be a powerful social glue. It wopuld also have left the edges of Christianity fuzzier if the distinction had carried less significance (in the 250s, demonstrating that you were a Manichaean, Jew, Gnostic or otherwise Not A Christian was a life and death matter rather than an academic exercise).
With less social unity I think would also come less doctrinal unity. Christian groups, defined by their tightly knit social networks, would still hold together over the medium term, but it is quite possiblew that, like many modern churches and cults similarly structured, they would be more amorphous than the highly regimented episcopal church of the patristic era.
As to conversions, I am not sure it would make too much of a difference. The idea that the blood of the martyrs is the seed of the church was a minority position initially. It is possible that fewer people would be attracted by a church that had not gone through the persecutions, but I think the added benefit of continued legal status would have made up for it. It might well have meant a different kind of recruit - seekers after strong certainties might be drawn elsewhere while noncomittally spiritual persons would probably seek out fuzzy-Christian circles. That would have an impact in the long run. But we must not forget that for most of the third century, Christian communities lived rather safely among their pagan neighbours, building large burial complexes, owning real estate, holding meetings, running charity networks and altogether being visible. That, not the huddled crowd of frightened worshippers you are admitted to through a furtively whispered secret password of Hollywood imagination, was the church people joined. That would still be there.
It might also well mean a lot less state cinterference. This church would be a relative nonentity to the emperors, unless and until one converted, and it would have a longer tradition of not being doctrinally united. If and how it could take over the role of state religion would be quite interesting.