As Ron indicates, flying without pitot heat in actual conditions is chancy, at best. And in Tennessee you'll certainly have plenty of wet conditions in IFR to make the pitot heat very desirable indeed.
And keep in mind that changing out the avionics can involve a fair amount of down time, in addition to the expense, depending on a number of factors such as who's doing the work, parts availabilty and what work actually needs doing, since older aircraft often need more work to install newer avionics than newer aircraft do.
So yes, you could get your instrument rating in that aircraft, but it's best to get some actual instrument time during training, if possible (sometimes it's not, here in the mountain west), and I'd not do it without that pitot heat.
So sometimes a "bargain" isn't...