LLM post-training with reinforcement learning (RL) requires frequent synchronization of large model parameters between the trainer and distributed rollout actors. High-throughput RL post-training therefore relies on dedicated RDMA HPC clusters, an infrastructure cost most organizations cannot absorb. A natural alternative is to aggregate loosely-coupled GPUs over standard Ethernet and WAN links, but this commodity connectivity cannot sustain full-weight broadcasts: synchronizing an 8B model can take over 100~seconds on bandwidth-limited links, while rollout generation typically takes tens of seconds. Toward making RL practical in this regime, we observe that RL fine-tuning yields highly sparse per-step updates, with only around 1\% of parameter elements changing. Atop this insight, we present SparrowRL, a novel high-performance RL training system that preserves bit-exact updates without dropping or quantizing information, designed for commodity-networked, loosely-coupled GPU resources. SparrowRL represents each step as a sparse delta checkpoint, pipelines delta extraction with multi-stream transmission, overlaps transfer with rollout generation, and coordinates heterogeneous workers with throughput- and bandwidth-aware scheduling plus lease-based fault tolerance. On Qwen3 models from 4B to 14B deployed across up to four geographic regions, SparrowRL reduces per-step transfer payload by 79$\times$ for Qwen3-8B and improves throughput by 2.4--9.5$\times$ over full-weight broadcast across WAN, narrowing the throughput gap relative to an ideal RDMA single-datacenter baseline to within 8.91\%. By leveraging on-demand, cross-cloud GPUs over commodity links, SparrowRL delivers 1.21--1.59$\times$ higher tokens per dollar than reserved RDMA clusters at comparable throughput.