You you want code review and testing, then start looking for another job right this moment. It doesn't matter whether the company has a right to crappy-but-working code. They are probably not going to change their standards until the situation with their software becomes untenable for them, so I wouldn't hold out hope that things will get better in X years.

In the mean time, see what standards you can implement without their permission. If you can fit some tests in there without sacrificing velocity, I see no reason not to add them. What are they gonna do? Tell you no? That will be a litmus test for whether you have any future with these people.