If for example the "eval" command is introduced in Dart, then the answer is YES, Dart is vulnerable to injection attacks.
Javascript is in this regard like SQL: it has the same vulnerability than all other dynamically interpreted programming languages (this includes all shell scripts, PHP...), which I call "DATA IS CODE". Such languages have a concrete syntax which is meant for human consumption and their processing entails a first step which is called PARSING: the sequence of characters is broken down into an internal structure which describes the meaning of the expression, in a way which the computer can distinguish the DATA from the INSTRUCTIONS. It is the same problem that lead to the introduction of the NX (No-eXecute) bit on modern CPUs. Functions like "eval" open the door to malicious code to be executed with no constraint. Parsing code at runtime should NEVER be allowed in a secure language.
This is why Dart doesn't recomend the use of injections, as explained here:
https://www.dartlang.org/articles/embedding-in-html/#no-script-injection-of-dart-code
"No script injection of Dart code We do not currently support or
recommend dynamically injecting a tag that loads Dart code.
Recent browser security trends, like Content Security Policy, actively
prevent this practice."
But google should do more than that, and forbid it entirely, together with the "eval" command.