The use of natural language (NL) test cases for validating graphical user interface (GUI) applications is emerging as a promising direction to manually written executable test scripts, which are costly to develop and difficult to maintain. Recent advances in large language models (LLMs) have opened the possibility of the direct execution of NL test cases by LLM agents. This paper investigates this direction, focusing on the impact on NL test case unsoundness and on test case execution consistency. NL test cases are inherently unsound, as they may yield false failures due to ambiguous instructions or unpredictable agent behaviour. Furthermore, repeated executions of the same NL test case may lead to inconsistent outcomes, undermining test reliability. To address these challenges, we propose an algorithm for executing NL test cases with guardrail mechanisms and specialised agents that dynamically verify the correct execution of each test step. We introduce measures to evaluate the capabilities of LLMs in test execution and one measure to quantify execution consistency. We propose a definition of weak unsoundness to characterise contexts in which NL test case execution remains acceptable, with respect to the industrial quality levels Six Sigma. Our experimental evaluation with eight publicly available LLMs, ranging from 3B to 70B parameters, demonstrates both the potential and current limitations of current LLM agents for GUI testing. Our experiments show that Meta Llama 3.1 70B demonstrates acceptable capabilities in NL test case execution with high execution consistency (above the level 3-sigma). We provide prototype tools, test suites, and results.