"Vieni e provalo!"
Kind of, it implies extra meaning because the listener must know what the speaker is referring to, come and try would better translate as "Vieni e prova".
Equally you could put qui with vieni "Vieni qui e provalo" to say come here and try it. It isn't always necessary to say here or it, in english, nor lo or qui in italian, because often they could be implied from the context. But when translating from one to the other, especially without the context like we have here, its best to include them.
Only if it were in present simple, but what is happening here is that they are both in the informal command tense. 'are' verbs like provare switch their formal and informal 2nd person singular endings in this tense, while 'ire/ere' ones like venire don't change for the informal. The result can look like a mixing of formal and informal at first glance when both types are in the one sentence.