I have two budgies and a tiel. Jerry was my first bird, and Lulu the tiel came home about 4 months later. And Winston came along about a year after that. Jerry was smitten with Lulu, but as budgies normally tend to be, they can be very pushy. He tried to be friends with her, but she wanted nothing to do with him. Basically, she doesn't want the budgie any closer than a foot from her. He tries to show her the budgie signs of affection - you know, knocking beaks and warbling in her face. She thinks that's appalling
But now that Winston is here, Jerry's attention is more on Winston. Lulu was his first love (besides me

yes, he wants all the ladies' attention lol) so he still does try to befriend her somewhat, but not near as much as he used to. Lulu tolerates the budgies pretty well - she still has no desire to play with them, she minds her own business.
I think you'd be fine if you got a tiel. I wouldn't expect the tiel to get along with the budgies (being friends and all), but I think the budgies would stick together. And I have heard that some people have had tiels and budgies get along - but I would assume that they don't because tiels generally have more laid back attitudes whereas budgies are more high strung and full of energy.
I would NOT house tiels and budgies together though, I think that's asking for trouble when the budgies are being the little pests that they can be.
Personally, based on my flock's behavior, I have decided that nothing larger than a tiel will come into the house as long as we have budgies (and we sure hope they are here for a long time to come!). A tiel's beak is very strong and can surely do damage - we ALWAYS supervise the birds when they are out every day. Although Lulu tolerates the budgies, supervision is required to make sure that no one gets hurt. I feel that Jerry would still try and approach a larger bird (he's very nosy!), and anything larger than Lulu would pose a great threat, IMO.